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- W4300922013 abstract "Let $M$ be an $n$-vertex combinatorial triangulation of a $ZZ_2$-homology $d$-sphere. In this paper we prove that if $n leq d + 8$ then $M$ must be a combinatorial sphere. Further, if $n = d + 9$ and $M$ is not a combinatorial sphere then $M$ can not admit any proper bistellar move. Existence of a 12-vertex triangulation of the lens space $L(3, 1)$ shows that the first result is sharp in dimension three. In the course of the proof we also show that any $ZZ_2$-acyclic simplicial complex on $leq 7$ vertices is necessarily collapsible. This result is best possible since there exist 8-vertex triangulations of the Dunce Hat which are not collapsible." @default.
- W4300922013 created "2022-10-04" @default.
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- W4300922013 date "2005-06-27" @default.
- W4300922013 modified "2023-09-23" @default.
- W4300922013 title "Combinatorial triangulations of homology spheres" @default.
- W4300922013 doi "https://doi.org/10.48550/arxiv.math/0506536" @default.
- W4300922013 hasPublicationYear "2005" @default.
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