{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:58:21Z","timestamp":1776833901488,"version":"3.51.2"},"reference-count":55,"publisher":"American Mathematical Society (AMS)","issue":"331","license":[{"start":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T00:00:00Z","timestamp":1651190400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"StartFraction 34 pi squared Over 3 EndFraction dot 16\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mfrac>\n                              <mml:mrow>\n                                <mml:mn>34<\/mml:mn>\n                                <mml:msup>\n                                  <mml:mi>\n                                    \u03c0\n                                    \n                                  <\/mml:mi>\n                                  <mml:mn>2<\/mml:mn>\n                                <\/mml:msup>\n                              <\/mml:mrow>\n                              <mml:mn>3<\/mml:mn>\n                            <\/mml:mfrac>\n                            <mml:mo>\n                              \u22c5\n                              \n                            <\/mml:mo>\n                            <mml:mn>16<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\frac {34\\pi ^2}{3}\\cdot 16<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    by using the small cover theory. In particular, we classify all of the orientable four-dimensional small covers over the right-angled 120-cell up to homeomorphism; these are all with even intersection forms.\n                  <\/p>","DOI":"10.1090\/mcom\/3625","type":"journal-article","created":{"date-parts":[[2020,12,23]],"date-time":"2020-12-23T11:27:16Z","timestamp":1608722836000},"page":"2463-2501","source":"Crossref","is-referenced-by-count":5,"title":["Orientable hyperbolic 4-manifolds over the 120-cell"],"prefix":"10.1090","volume":"90","author":[{"given":"Jiming","family":"Ma","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fangting","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2021,4,29]]},"reference":[{"issue":"2","key":"1","first-page":"219","article-title":"Dehn filling and Einstein metrics in higher dimensions","volume":"73","author":"Anderson, Michael T.","year":"2006","journal-title":"J. Differential Geom.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-040X","issn-type":"print"},{"key":"2","unstructured":"D. Barali\u0107 and L. Milenkovi\u0107, Surprising examples of manifolds in toric topology!,  arXiv:1704.05932, 2017."},{"key":"3","series-title":"Mathematical Surveys and Monographs","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/204","volume-title":"Toric topology","volume":"204","author":"Buchstaber, Victor M.","year":"2015","ISBN":"https:\/\/id.crossref.org\/isbn\/9781470422141"},{"issue":"2","key":"4","doi-asserted-by":"publisher","first-page":"503","DOI":"10.2969\/jmsj\/06920503","article-title":"On products in a real moment-angle manifold","volume":"69","author":"Cai, Li","year":"2017","journal-title":"J. Math. Soc. Japan","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5645","issn-type":"print"},{"key":"5","unstructured":"L. Cai and S. Choi, Integral cohomology groups of real toric manifolds and small covers,  arXiv:1604.06988, 2016."},{"issue":"4","key":"6","doi-asserted-by":"publisher","first-page":"2391","DOI":"10.2140\/agt.2008.8.2391","article-title":"The number of small covers over cubes","volume":"8","author":"Choi, Suyoung","year":"2008","journal-title":"Algebr. Geom. Topol.","ISSN":"https:\/\/id.crossref.org\/issn\/1472-2747","issn-type":"print"},{"issue":"4","key":"7","doi-asserted-by":"publisher","first-page":"2987","DOI":"10.1090\/tran\/6896","article-title":"Classification of real Bott manifolds and acyclic digraphs","volume":"369","author":"Choi, Suyoung","year":"2017","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1515\/forum-2016-0025","article-title":"On the cohomology and their torsion of real toric objects","volume":"29","author":"Choi, Suyoung","year":"2017","journal-title":"Forum Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0933-7741","issn-type":"print"},{"key":"9","unstructured":"S. Choi and H. Park. Multiplication structure of the cohomology ring of real toric spaces.  arXiv:1711.04983v1."},{"issue":"249","key":"10","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1090\/S0025-5718-04-01647-3","article-title":"Applications and adaptations of the low index subgroups procedure","volume":"74","author":"Conder, Marston","year":"2005","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"8","key":"11","doi-asserted-by":"publisher","first-page":"2469","DOI":"10.1090\/S0002-9939-05-07634-3","article-title":"Compact hyperbolic 4-manifolds of small volume","volume":"133","author":"Conder, Marston","year":"2005","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"key":"12","volume-title":"Introduction to geometry","author":"Coxeter, H. S. M.","year":"1969","edition":"2"},{"issue":"2","key":"13","doi-asserted-by":"publisher","first-page":"325","DOI":"10.2307\/2044771","article-title":"A hyperbolic 4-manifold","volume":"93","author":"Davis, Michael W.","year":"1985","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"issue":"2","key":"14","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1215\/S0012-7094-91-06217-4","article-title":"Convex polytopes, Coxeter orbifolds and torus actions","volume":"62","author":"Davis, Michael W.","year":"1991","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"},{"issue":"3","key":"15","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/BF01389358","article-title":"Torsion free subgroups of Fuchsian groups and tessellations of surfaces","volume":"69","author":"Edmonds, Allan L.","year":"1982","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"3","key":"16","doi-asserted-by":"publisher","first-page":"871","DOI":"10.1007\/s00208-011-0744-2","article-title":"Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel","volume":"354","author":"Everitt, Brent","year":"2012","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"issue":"2","key":"17","first-page":"227","article-title":"Small covers over L\u00f6bell polytopes","volume":"38","author":"Fu, Xin","year":"2017","journal-title":"Chinese Ann. Math. Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/1000-8314","issn-type":"print"},{"issue":"4","key":"18","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1090\/S0894-0347-09-00639-0","article-title":"Minimum volume cusped hyperbolic three-manifolds","volume":"22","author":"Gabai, David","year":"2009","journal-title":"J. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0894-0347","issn-type":"print"},{"issue":"2","key":"19","doi-asserted-by":"publisher","first-page":"335","DOI":"10.4007\/annals.2003.157.335","article-title":"Homotopy hyperbolic 3-manifolds are hyperbolic","volume":"157","author":"Gabai, David","year":"2003","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"3","key":"20","doi-asserted-by":"publisher","first-page":"963","DOI":"10.1090\/S0002-9939-02-06577-2","article-title":"Small covers of the dodecahedron and the 120-cell","volume":"131","author":"Garrison, Anne","year":"2003","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"key":"21","series-title":"Graduate Studies in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/020","volume-title":"$4$-manifolds and Kirby calculus","volume":"20","author":"Gompf, Robert E.","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/0821809946"},{"key":"22","first-page":"171","article-title":"Cohen-Macaulay rings, combinatorics, and simplicial complexes","author":"Hochster, Melvin","year":"1977"},{"key":"23","doi-asserted-by":"crossref","unstructured":"I. Izmestiev. Three dimensional manifolds defined by coloring a simple polytope. Math. Notes, 69 (2001), 340\u2013346.","DOI":"10.1023\/A:1010231424507"},{"key":"24","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1016\/j.jcta.2018.04.001","article-title":"All hyperbolic Coxeter \ud835\udc5b-cubes","volume":"158","author":"Jacquemet, Matthieu","year":"2018","journal-title":"J. Combin. Theory Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0097-3165","issn-type":"print"},{"issue":"2","key":"25","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s002080050147","article-title":"Minimal index torsion-free subgroups of Kleinian groups","volume":"310","author":"Jones, Kerry N.","year":"1998","journal-title":"Math. Ann.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5831","issn-type":"print"},{"issue":"3","key":"26","doi-asserted-by":"publisher","first-page":"Paper No. 48, 39","DOI":"10.1007\/s00029-019-0492-9","article-title":"Commensurability classes of fake quadrics","volume":"25","author":"Linowitz, Benjamin","year":"2019","journal-title":"Selecta Math. (N.S.)","ISSN":"https:\/\/id.crossref.org\/issn\/1022-1824","issn-type":"print"},{"issue":"11","key":"27","doi-asserted-by":"publisher","first-page":"1742","DOI":"10.1007\/s10114-018-7160-4","article-title":"Cellular chain complex of small covers with integer coefficients and its application","volume":"34","author":"Liu, Deng Pin","year":"2018","journal-title":"Acta Math. Sin. (Engl. Ser.)","ISSN":"https:\/\/id.crossref.org\/issn\/1439-8516","issn-type":"print"},{"issue":"5","key":"28","doi-asserted-by":"publisher","first-page":"913","DOI":"10.1112\/blms\/bdn077","article-title":"Small volume closed hyperbolic 4-manifolds","volume":"40","author":"Long, C.","year":"2008","journal-title":"Bull. Lond. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"key":"29","doi-asserted-by":"publisher","first-page":"171","DOI":"10.2140\/gt.2000.4.171","article-title":"On the geometric boundaries of hyperbolic 4-manifolds","volume":"4","author":"Long, D. D.","year":"2000","journal-title":"Geom. Topol.","ISSN":"https:\/\/id.crossref.org\/issn\/1465-3060","issn-type":"print"},{"issue":"6","key":"30","doi-asserted-by":"publisher","first-page":"1311","DOI":"10.1007\/s11401-007-1039-5","article-title":"Torsions of 3-dimensional small covers","volume":"38","author":"Ma, Jiming","year":"2017","journal-title":"Chinese Ann. Math. Ser. B","ISSN":"https:\/\/id.crossref.org\/issn\/0252-9599","issn-type":"print"},{"key":"31","unstructured":"J. Ma and F. Zheng, Geometrically bounding 3-manifold, volume and Betti number, To appear in Algebr. Geom. Topol. \\url{https:\/\/msp.org\/soon\/coming.php?jpath=agt}"},{"issue":"1","key":"32","doi-asserted-by":"publisher","first-page":"261","DOI":"10.4007\/annals.2012.176.1.4","article-title":"Minimal co-volume hyperbolic lattices, II: Simple torsion in a Kleinian group","volume":"176","author":"Marshall, T. H.","year":"2012","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"33","isbn-type":"print","first-page":"37","article-title":"Hyperbolic four-manifolds","author":"Martelli, Bruno","year":"2018","ISBN":"https:\/\/id.crossref.org\/isbn\/9781571463647"},{"issue":"5","key":"34","doi-asserted-by":"publisher","first-page":"2647","DOI":"10.2140\/gt.2020.24.2647","article-title":"Compact hyperbolic manifolds without spin structures","volume":"24","author":"Martelli, Bruno","year":"2020","journal-title":"Geom. Topol.","ISSN":"https:\/\/id.crossref.org\/issn\/1465-3060","issn-type":"print"},{"issue":"3","key":"35","doi-asserted-by":"publisher","first-page":"1647","DOI":"10.2140\/gt.2018.22.1647","article-title":"Hyperbolic Dehn filling in dimension four","volume":"22","author":"Martelli, Bruno","year":"2018","journal-title":"Geom. Topol.","ISSN":"https:\/\/id.crossref.org\/issn\/1465-3060","issn-type":"print"},{"issue":"3","key":"36","first-page":"Article 04.3.3, 5","article-title":"Acyclic digraphs and eigenvalues of (0,1)-matrices","volume":"7","author":"McKay, Brendan D.","year":"2004","journal-title":"J. Integer Seq."},{"issue":"1","key":"37","first-page":"243","article-title":"The orientability of small covers and coloring simple polytopes","volume":"42","author":"Nakayama, Hisashi","year":"2005","journal-title":"Osaka J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0030-6126","issn-type":"print"},{"issue":"306","key":"38","doi-asserted-by":"publisher","first-page":"1979","DOI":"10.1090\/mcom\/3147","article-title":"On the arithmetic dimension of triangle groups","volume":"86","author":"Nugent, Steve","year":"2017","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"39","doi-asserted-by":"publisher","first-page":"63","DOI":"10.4171\/CMH\/4","article-title":"On right-angled reflection groups in hyperbolic spaces","volume":"80","author":"Potyagailo, Leonid","year":"2005","journal-title":"Comment. Math. Helv.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-2571","issn-type":"print"},{"issue":"1","key":"40","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1080\/10586458.2000.10504640","article-title":"The volume spectrum of hyperbolic 4-manifolds","volume":"9","author":"Ratcliffe, John G.","year":"2000","journal-title":"Experiment. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1058-6458","issn-type":"print"},{"issue":"3","key":"41","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/S0166-8641(99)00221-7","article-title":"On the Davis hyperbolic 4-manifold","volume":"111","author":"Ratcliffe, John G.","year":"2001","journal-title":"Topology Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0166-8641","issn-type":"print"},{"key":"42","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s10711-004-8120-y","article-title":"Integral congruence two hyperbolic 5-manifolds","volume":"107","author":"Ratcliffe, John G.","year":"2004","journal-title":"Geom. Dedicata","ISSN":"https:\/\/id.crossref.org\/issn\/0046-5755","issn-type":"print"},{"key":"43","first-page":"391","article-title":"Enumeration of acyclic digraphs","author":"Robinson, Robert W.","year":"1970"},{"key":"44","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/j.topol.2016.01.024","article-title":"Kirby diagrams and the Ratcliffe-Tschantz hyperbolic 4-manifolds","volume":"202","author":"Saratchandran, Hemanth","year":"2016","journal-title":"Topology Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0166-8641","issn-type":"print"},{"key":"45","unstructured":"H. Saratchandran, A four dimensional hyperbolic link complement in a standard \ud835\udc46\u2074,  arXiv:1503.07778, 2015."},{"key":"46","unstructured":"H. Saratchandran, A four dimensional hyperbolic link complement in a standard \ud835\udc46\u00b2\u00d7\ud835\udc46\u00b2,  arXiv:1504.01366, 2015."},{"key":"47","unstructured":"H. Saratchandran, Complements of tori in #_{2\ud835\udc58}\ud835\udc46\u00b2\u00d7\ud835\udc46\u00b2 that admit a hyperbolic structure,  arXiv:1504.06703, 2015."},{"issue":"11","key":"48","doi-asserted-by":"publisher","first-page":"1309","DOI":"10.1090\/noti1297","article-title":"Puzzling the 120-cell","volume":"62","author":"Schleimer, Saul","year":"2015","journal-title":"Notices Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9920","issn-type":"print"},{"key":"49","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/0012-365X(73)90108-8","article-title":"Acyclic orientations of graphs","volume":"5","author":"Stanley, Richard P.","year":"1973","journal-title":"Discrete Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-365X","issn-type":"print"},{"key":"50","unstructured":"A. I. Suciu. The rational homology of real toric manifolds.  arXiv:1302.2342v1(2013)."},{"key":"51","unstructured":"A. I. Suciu and Alvise Trevisan. Real toric varieties and abelian covers of generalized Davis-Januszkiewicz spaces. Preprint, 2012."},{"issue":"1","key":"52","doi-asserted-by":"publisher","first-page":"205","DOI":"10.4310\/HHA.2011.v13.n1.a8","article-title":"Generalized Davis-Januszkiewicz spaces, multicomplexes and monomial rings","volume":"13","author":"Trevisan, Alvise J.","year":"2011","journal-title":"Homology Homotopy Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/1532-0073","issn-type":"print"},{"issue":"5","key":"53","first-page":"50","article-title":"Three-dimensional hyperbolic manifolds of L\u00f6bell type","volume":"28","author":"Vesnin, A. Yu.","year":"1987","journal-title":"Sibirsk. Mat. Zh.","ISSN":"https:\/\/id.crossref.org\/issn\/0037-4474","issn-type":"print"},{"issue":"6","key":"54","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/BF01156579","article-title":"Three-dimensional hyperbolic manifolds with a common fundamental polyhedron","volume":"49","author":"Vesnin, A. Yu.","year":"1991","journal-title":"Mat. Zametki","ISSN":"https:\/\/id.crossref.org\/issn\/0025-567X","issn-type":"print"},{"issue":"2","key":"55","doi-asserted-by":"publisher","first-page":"147","DOI":"10.4213\/rm9762","article-title":"Right-angled polytopes and three-dimensional hyperbolic manifolds","volume":"72","author":"Vesnin, A. Yu.","year":"2017","journal-title":"Uspekhi Mat. Nauk","ISSN":"https:\/\/id.crossref.org\/issn\/0042-1316","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/earlyview\/#mcom3625\/.pdf","content-type":"unspecified","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2021-90-331\/S0025-5718-2021-03625-X\/S0025-5718-2021-03625-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:13:58Z","timestamp":1776831238000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2021-90-331\/S0025-5718-2021-03625-X\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,29]]},"references-count":55,"journal-issue":{"issue":"331","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["S0025-5718-2021-03625-X"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3625","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2021,4,29]]}}}