On Stacked Triangulated Manifolds

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 $d \geq 4$, if $\Delta$ is a tight conn...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2017-10, Vol.24 (4)
Main Authors: Datta, Basudeb, Murai, Satoshi
Format: Article
Language:English
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Summary: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 $d \geq 4$, if $\Delta$ is a tight connected closed homology $d$-manifold whose $i$th homology vanishes for $1 < i < d-1$, then $\Delta$ is a stacked triangulation of a manifold. These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger. 
ISSN:1077-8926
1077-8926
DOI:10.37236/6181