{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:46:08Z","timestamp":1787237168794,"version":"3.56.0"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"Friends of the Institute for Advanced Study"},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["422182"],"award-info":[{"award-number":["422182"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/R018472\/1"],"award-info":[{"award-number":["EP\/R018472\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Algebra Geometry"],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We introduce and analyze parallelizable algorithms to compress and accurately reconstruct finite simplicial complexes that have nontrivial automorphisms. The compressed data---called a complex of groups---amounts to a functor from (the poset of simplices in) the orbit space to the 2-category of groups, whose higher structure is prescribed by isomorphisms arising from conjugation. Using this functor, we show how to algorithmically recover the original complex up to equivariant simplicial isomorphism. Our algorithms are derived from generalizations (by Bridson--Haefliger, Carbone--Rips, and Corson, among others) of the classical Bass--Serre theory for reconstructing group actions on trees.<\/jats:p>","DOI":"10.1137\/20m1327483","type":"journal-article","created":{"date-parts":[[2020,12,14]],"date-time":"2020-12-14T10:59:22Z","timestamp":1607943562000},"page":"532-552","source":"Crossref","is-referenced-by-count":1,"title":["Equivariant Simplicial Reconstruction"],"prefix":"10.1137","volume":"4","author":[{"given":"Lisa","family":"Carbone","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vidit","family":"Nanda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yusra","family":"Naqvi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,12,14]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2001.07.002"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(93)90085-8"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1162\/089976603321780317"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"atypb5","unstructured":"G. E. Bredon,\n                      Introduction to Compact Transformation Groups\n                      , Pure Appl. Math. 46, Academic Press, New York, London, 1972."},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"M. R. Bridson and A. Haefliger,\n                      Metric Spaces of Non-positive Curvature\n                      , Grundlehren Math. Wiss. 319, Springer-Verlag, Berlin, 1999.","DOI":"10.1007\/978-3-662-12494-9"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1142\/S021819671340002X"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2010.04.022"},{"key":"atypb9","unstructured":"I. Chevyrev and A. Kormilitzin,\n                      A Primer on the Signature Method in Machine Learning\n                      , preprint,https:\/\/arxiv.org\/abs\/1603.03788, 2016."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-65.1.199"},{"key":"atypb11","unstructured":"J. Curry,\n                      Sheaves, Cosheaves and Applications\n                      , preprint,https:\/\/arxiv.org\/abs\/1303.3255, 2013."},{"key":"atypb12","unstructured":"M. W. Davis,\n                      The Geometry and Topology of Coxeter Groups\n                      , Princeton University Press, Princeton, NJ, 2008."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2014.2346172"},{"key":"atypb14","unstructured":"W. Dicks and M. J. Dunwoody,\n                      Groups Acting on Graphs\n                      , Cambridge Stud. Adv. Math. 17, Cambridge University Press, Cambridge, 1989."},{"key":"atypb15","doi-asserted-by":"crossref","first-page":"301","DOI":"10.4171\/dm\/333","volume":"16","author":"Fiore T.","year":"2011","journal-title":"Doc. Math."},{"key":"atypb16","unstructured":"T. Gao, J. Brodzki, and S. Mukherjee,\n                      The Geometry of Synchronization Problems and Learning Group Actions\n                      , preprint,https:\/\/arxiv.org\/abs\/1610.09051, 2016."},{"key":"atypb17","first-page":"61","volume":"45","author":"Ghrist R.","year":"2009","journal-title":"S.)"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s11784-012-0087-y"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.5802\/aif.1292"},{"key":"atypb20","unstructured":"A. Hatcher,\n                      Algebraic Topology\n                      , Cambridge University Press, Cambridge, 2002."},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"D. F. Holt, B. Eick, and E. A. O'Brien,\n                      Handbook of Computational Group Theory\n                      , Chapman and Hall\/CRC, Boca Raton, FL, 2005.","DOI":"10.1201\/9781420035216"},{"key":"atypb22","unstructured":"T. W. Hungerford,\n                      Algebra\n                      , Grad. Texts in Math. 73, Springer-Verlag, New York, Berlin, 1980."},{"key":"atypb23","unstructured":"S. Krishnan,\n                      Flow-Cut Dualities for Sheaves on Graphs\n                      , preprint,https:\/\/arxiv.org\/abs\/1409.6712, 2014."},{"key":"atypb24","first-page":"105","author":"Lack S.","year":"2010","journal-title":"New York"},{"key":"atypb25","unstructured":"T. Leinster,\n                      Basic Bicategories\n                      , preprint,https:\/\/arxiv.org\/abs\/math\/9810017, 1998."},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2007.10.012"},{"key":"atypb27","doi-asserted-by":"crossref","unstructured":"S. Mac Lane,\n                      Categories for the Working Mathematician\n                      , Grad. Texts in Math. 5, Springer-Verlag, New York, Berlin, 1971.","DOI":"10.1007\/978-1-4612-9839-7"},{"key":"atypb28","first-page":"47","volume":"1","author":"Martins-Ferreira N.","year":"2006","journal-title":"J. Homotopy Relat. Struct."},{"key":"atypb29","first-page":"560","author":"Mitra N. J.","year":"2006","journal-title":"New York"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1023\/A:1007767628271"},{"key":"atypb31","first-page":"269","volume":"10","author":"Moerdijk I.","year":"1999","journal-title":"S.)"},{"key":"atypb32","unstructured":"B. Noohi,\n                      Foundations of Topological Stacks I\n                      , preprint,https:\/\/arxiv.org\/abs\/math\/0503247, 2005."},{"key":"atypb33","unstructured":"J.P. Serre,\n                      Trees\n                      , translated from the French by John Stillwell, Springer-Verlag, Berlin, 1980."},{"key":"atypb34","doi-asserted-by":"crossref","unstructured":"E. H. Spanier,\n                      Algebraic Topology\n                      , McGraw-Hill, New York, Toronto, London 1966.","DOI":"10.1007\/978-1-4684-9322-1_5"}],"container-title":["SIAM Journal on Applied Algebra and Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1327483","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:17:41Z","timestamp":1787235461000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1327483"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":34,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/20M1327483"],"URL":"https:\/\/doi.org\/10.1137\/20m1327483","relation":{},"ISSN":["2470-6566"],"issn-type":[{"value":"2470-6566","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}