On stacked triangulated manifolds

Basudeb Datta; Satoshi Murai

doi:10.37236/6181

On stacked triangulated manifolds

Basudeb Datta, Satoshi Murai

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) in dimension d ≥ 4, if Δ is a tight connected closed homology d-manifold whose ith homology vanishes for 1 < i < d - 1, then Δ is a stacked triangulation of a manifold. These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger.

Original language	English
Article number	#P4.12
Journal	Electronic Journal of Combinatorics
Volume	24
Issue number	4
DOIs	https://doi.org/10.37236/6181
Publication status	Published - 2017 Oct 6
Externally published	Yes

Keywords

Stacked manifolds
Tight triangulations
Triangulations of 3-manifolds

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/6181

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abstract = "We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) in dimension d ≥ 4, if Δ is a tight connected closed homology d-manifold whose ith homology vanishes for 1 < i < d - 1, then Δ is a stacked triangulation of a manifold. These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger.",

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author = "Basudeb Datta and Satoshi Murai",

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AU - Murai, Satoshi

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N2 - We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) in dimension d ≥ 4, if Δ is a tight connected closed homology d-manifold whose ith homology vanishes for 1 < i < d - 1, then Δ is a stacked triangulation of a manifold. These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger.

AB - We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) in dimension d ≥ 4, if Δ is a tight connected closed homology d-manifold whose ith homology vanishes for 1 < i < d - 1, then Δ is a stacked triangulation of a manifold. These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger.

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KW - Tight triangulations

KW - Triangulations of 3-manifolds

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On stacked triangulated manifolds

Abstract

Keywords

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