{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T09:27:49Z","timestamp":1773739669570,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,7,1]],"date-time":"2014-07-01T00:00:00Z","timestamp":1404172800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2014,7]]},"DOI":"10.1007\/s00454-014-9572-y","type":"journal-article","created":{"date-parts":[[2014,7,9]],"date-time":"2014-07-09T13:06:15Z","timestamp":1404911175000},"page":"116-139","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A New Approach to Crushing 3-Manifold Triangulations"],"prefix":"10.1007","volume":"52","author":[{"given":"Benjamin A.","family":"Burton","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,7,10]]},"reference":[{"key":"9572_CR1","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1142\/9789812777171_0020","volume-title":"Mathematical Software: Proceedings of the First International Congress of Mathematical Software","author":"M.V. Andreeva","year":"2002","unstructured":"Andreeva, M.V., Dynnikov, I.A., Polthier, K.: A mathematical webservice for recognizing the unknot. In: Mathematical Software: Proceedings of the First International Congress of Mathematical Software, pp. 201\u2013207. World Scientific, Singapore (2002)"},{"issue":"8","key":"9572_CR2","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1142\/S0218216504003627","volume":"13","author":"B.A. Burton","year":"2004","unstructured":"Burton, B.A.: Face pairing graphs and 3-manifold enumeration. J. Knot Theory Ramif. 13(8), 1057\u20131101 (2004)","journal-title":"J. Knot Theory Ramif."},{"issue":"3","key":"9572_CR3","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1080\/10586458.2004.10504538","volume":"13","author":"B.A. Burton","year":"2004","unstructured":"Burton, B.A.: Introducing Regina, the 3-manifold topology software. Exp. Math. 13(3), 267\u2013272 (2004)","journal-title":"Exp. Math."},{"issue":"3","key":"9572_CR4","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1080\/10586458.2010.10390625","volume":"19","author":"B.A. Burton","year":"2010","unstructured":"Burton, B.A.: Quadrilateral-octagon coordinates for almost normal surfaces. Exp. Math. 19(3), 285\u2013315 (2010)","journal-title":"Exp. Math."},{"key":"9572_CR5","series-title":"Contemporary Mathematics","volume-title":"Geometry and Topology Down Under","author":"B.A. Burton","year":"2013","unstructured":"Burton, B.A.: Computational topology with Regina: algorithms, heuristics and implementations. In: Hodgson, C.D., Jaco, W.H., Scharlemann, M.G., Tillmann, S. (eds.) Geometry and Topology Down Under. Contemporary Mathematics, vol. 597. Am. Math. Soc., Providence (2013)"},{"key":"9572_CR6","unstructured":"Burton, B.A., Ozlen, M.: A fast branching algorithm for unknot recognition with experimental polynomial-time behaviour. Preprint arXiv:1211.1079 , November 2012"},{"issue":"2","key":"9572_CR7","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1090\/S0002-9947-2011-05419-X","volume":"364","author":"B.A. Burton","year":"2012","unstructured":"Burton, B.A., Rubinstein, J.H., Tillmann, S.: The Weber\u2013Seifert dodecahedral space is non-Haken. Trans. Am. Math. Soc. 364(2), 911\u2013932 (2012)","journal-title":"Trans. Am. Math. Soc."},{"key":"9572_CR8","first-page":"405","volume-title":"SCG\u201913: Proceedings of the 29th Annual Symposium on Computational Geometry","author":"B.A. Burton","year":"2013","unstructured":"Burton, B.A., Coward, A., Tillmann, S.: Computing closed essential surfaces in knot complements. In: SCG\u201913: Proceedings of the 29th Annual Symposium on Computational Geometry, pp. 405\u2013414. ACM, New York (2013)"},{"key":"9572_CR9","unstructured":"Burton, B.A., Budney, R., Pettersson, W., et\u00a0al.: Regina: software for 3-manifold topology and normal surface theory (1999\u20132013). http:\/\/regina.sourceforge.net\/"},{"key":"9572_CR10","first-page":"650","volume-title":"32nd Annual Symposium on Foundations of Computer Science, San Juan, PR, 1991","author":"B.R. Donald","year":"1991","unstructured":"Donald, B.R., Chang, D.R.: On the complexity of computing the homology type of a triangulation. In: 32nd Annual Symposium on Foundations of Computer Science, San Juan, PR, 1991, pp. 650\u2013661. IEEE Comput. Soc., Los Alamitos (1991)"},{"key":"9572_CR11","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/978-3-662-05148-1_10","volume-title":"Algebra, Geometry, and Software Systems","author":"J.-G. Dumas","year":"2003","unstructured":"Dumas, J.-G., Heckenbach, F., Saunders, D., Welker, V.: Computing simplicial homology based on efficient Smith normal form algorithms. In: Algebra, Geometry, and Software Systems, pp. 177\u2013206. Springer, Berlin (2003)"},{"key":"9572_CR12","unstructured":"Fowler, J.: Finding 0-efficient triangulations of 3-manifolds. Senior honors thesis, Harvard University (2003)"},{"key":"9572_CR13","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BF02559591","volume":"105","author":"W. Haken","year":"1961","unstructured":"Haken, W.: Theorie der Normalfl\u00e4chen. Acta Math. 105, 245\u2013375 (1961)","journal-title":"Acta Math."},{"key":"9572_CR14","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/BF01162369","volume":"80","author":"W. Haken","year":"1962","unstructured":"Haken, W.: \u00dcber das Hom\u00f6omorphieproblem der 3-Mannigfaltigkeiten. I. Math. Z. 80, 89\u2013120 (1962)","journal-title":"Math. Z."},{"key":"9572_CR15","volume-title":"Lecture Notes","author":"W. Jaco","year":"2005","unstructured":"Jaco, W.: The homeomorphism problem: classification of 3-manifolds. In: Lecture Notes (2005). Available from http:\/\/www.math.okstate.edu\/~jaco\/pekinglectures.htm"},{"issue":"1","key":"9572_CR16","doi-asserted-by":"crossref","first-page":"61","DOI":"10.4310\/jdg\/1090503053","volume":"65","author":"W. Jaco","year":"2003","unstructured":"Jaco, W., Hyam Rubinstein, J.: 0-efficient triangulations of 3-manifolds. J. Differ. Geom. 65(1), 61\u2013168 (2003)","journal-title":"J. Differ. Geom."},{"issue":"4","key":"9572_CR17","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1016\/S0040-9383(02)00083-6","volume":"42","author":"W. Jaco","year":"2003","unstructured":"Jaco, W., Sedgwick, E.: Decision problems in the space of Dehn fillings. Topology 42(4), 845\u2013906 (2003)","journal-title":"Topology"},{"issue":"3","key":"9572_CR18","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1215\/ijm\/1255986385","volume":"39","author":"W. Jaco","year":"1995","unstructured":"Jaco, W., Tollefson, J.L.: Algorithms for the complete decomposition of a closed 3-manifold. Ill. J. Math. 39(3), 358\u2013406 (1995)","journal-title":"Ill. J. Math."},{"issue":"2","key":"9572_CR19","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.2140\/gt.2011.15.1029","volume":"15","author":"T. Li","year":"2011","unstructured":"Li, T.: An algorithm to determine the Heegaard genus of a 3-manifold. Geom. Topol. 15(2), 1029\u20131106 (2011)","journal-title":"Geom. Topol."},{"issue":"2","key":"9572_CR20","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1080\/10586458.2001.10504444","volume":"10","author":"B. Martelli","year":"2001","unstructured":"Martelli, B., Petronio, C.: Three-manifolds having complexity at most 9. Exp. Math. 10(2), 207\u2013236 (2001)","journal-title":"Exp. Math."},{"key":"9572_CR21","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1215\/ijm\/1258130983","volume":"46","author":"B. Martelli","year":"2002","unstructured":"Martelli, B., Petronio, C.: A new decomposition theorem for 3-manifolds. Ill. J. Math. 46, 755\u2013780 (2002)","journal-title":"Ill. J. Math."},{"issue":"2","key":"9572_CR22","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF00049576","volume":"19","author":"S.V. Matveev","year":"1990","unstructured":"Matveev, S.V.: Complexity theory of three-dimensional manifolds. Acta Appl. Math. 19(2), 101\u2013130 (1990)","journal-title":"Acta Appl. Math."},{"key":"9572_CR23","volume-title":"Max-Planck-Institut f\u00fcr Mathematik Preprint Series","author":"S.V. Matveev","year":"1998","unstructured":"Matveev, S.V.: Tables of 3-manifolds up to complexity 6. In: Max-Planck-Institut f\u00fcr Mathematik Preprint Series, vol. 67 (1998). Available from http:\/\/www.mpim-bonn.mpg.de\/html\/preprints\/preprints.html"},{"key":"9572_CR24","series-title":"Algorithms and Computation in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-05102-3","volume-title":"Algorithmic Topology and Classification of 3-Manifolds","author":"S. Matveev","year":"2003","unstructured":"Matveev, S.: Algorithmic Topology and Classification of 3-Manifolds. Algorithms and Computation in Mathematics, vol. 9. Springer, Berlin (2003)"},{"key":"9572_CR25","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1007\/978-3-0348-9078-6_54","volume-title":"Proceedings of the International Congress of Mathematicians, Z\u00fcrich, 1994","author":"J.H. Rubinstein","year":"1995","unstructured":"Rubinstein, J.H.: An algorithm to recognize the 3-sphere. In: Proceedings of the International Congress of Mathematicians, Z\u00fcrich, 1994, vol. 1, pp. 601\u2013611. Birkh\u00e4user, Basel (1995)"},{"issue":"1","key":"9572_CR26","first-page":"75","volume":"28","author":"J.H. Rubinstein","year":"2004","unstructured":"Rubinstein, J.H.: An algorithm to recognise small Seifert fiber spaces. Turk. J. Math. 28(1), 75\u201387 (2004)","journal-title":"Turk. J. Math."},{"key":"9572_CR27","series-title":"Lecture Notes","volume-title":"The Geometry and Topology of Three-Manifolds","author":"W.P. Thurston","year":"1978","unstructured":"Thurston, W.P.: The Geometry and Topology of Three-Manifolds. Lecture Notes. Princeton University Press, Princeton (1978)"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-014-9572-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-014-9572-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-014-9572-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,15]],"date-time":"2023-07-15T03:12:54Z","timestamp":1689390774000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-014-9572-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["9572"],"URL":"https:\/\/doi.org\/10.1007\/s00454-014-9572-y","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7]]}}}