Face numbers of manifolds with boundary

Satoshi Murai, Isabella Novik*

*この研究の対応する著者

研究成果: Article査読

7 被引用数 (Scopus)

抄録

We study face numbers of simplicial complexes that triangulate manifolds (or even normal pseudomanifolds) with boundary. Specifically, we establish a sharp lower bound on the number of interior edges of a simplicial normal pseudomanifold with boundary in terms of the number of interior vertices and relative Betti numbers. Moreover, for triangulations of manifolds with boundary all of whose vertex links have the weak Lefschetz property, we extend this resultto sharp lower bounds onthe number of higher-dimensional interior faces. Along the way we develop a version of Bagchi and Datta's σ-and μ-numbers for the case of relative simplicial complexes and prove stronger versions of the above statements with the Betti numbers replaced by the μ-numbers. Our results provide natural generalizations of known theorems and conjectures for closed manifolds and appear to be new even for the case of a ball.

本文言語English
ページ(範囲)3603-3646
ページ数44
ジャーナルInternational Mathematics Research Notices
2017
12
DOI
出版ステータスPublished - 2017
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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