Abstract:
The question of the existence of an algorithm for determining whether given 3-manifolds are homeomorphic is a key question of low-dimensional topology. An algorithm due to A. Thompson for the recognition of the standard 3-sphere is presented. The use of handle decomposition instead of triangulation greatly simplifies both the formulation and the proof of the algorithm.
\Bibitem{Mat95}
\by S.~V.~Matveev
\paper An algorithm for the~recognition of 3-spheres (according to~Thompson)
\jour Sb. Math.
\yr 1995
\vol 186
\issue 5
\pages 695--710
\mathnet{http://mi.mathnet.ru/eng/sm37}
\crossref{https://doi.org/10.1070/SM1995v186n05ABEH000037}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1341085}
\zmath{https://zbmath.org/?q=an:0849.57010}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TC19700004}
Linking options:
https://www.mathnet.ru/eng/sm37
https://doi.org/10.1070/SM1995v186n05ABEH000037
https://www.mathnet.ru/eng/sm/v186/i5/p69
This publication is cited in the following 18 articles:
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DAVID BACHMAN, SAUL SCHLEIMER, “THIN POSITION FOR TANGLES”, J. Knot Theory Ramifications, 12:01 (2003), 117
Matveev S., Fominykh E., “Normal Surfaces in 3-Manifolds”, Dokl. Math., 65:3 (2002), 429–432
Simon A King, “The size of triangulations supporting a given link”, Geom Topol, 5 (2001), 369
Ivanov S., “Recognizing the 3-Sphere”, Ill. J. Math., 45:4 (2001), 1073–1117
S. I. Adian, V. G. Durnev, “Decision problems for groups and semigroups”, Russian Math. Surveys, 55:2 (2000), 207–296
Matveev, SV, “Computer classification of 3-manifolds”, Russian Journal of Mathematical Physics, 7:3 (2000), 319
Stocking M., “Almost Normal Surfaces in 3-Manifolds”, Trans. Am. Math. Soc., 352:1 (2000), 171–207
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