Tight combinatorial manifolds and graded Betti numbers

Satoshi Murai*

*この研究の対応する著者

研究成果: Article査読

17 被引用数 (Scopus)

抄録

In this paper, we study the conjecture of Kühnel and Lutz, who state that a combinatorial triangulation of the product of two spheres Si×Sj with j ≥ i is tight if and only if it has exactly i + 2j + 4 vertices. To approach this conjecture, we use graded Betti numbers of Stanley–Reisner rings. By using recent results on graded Betti numbers, we prove that the only if part of the conjecture holds when j > 2i and that the if part of the conjecture holds for triangulations all whose vertex links are simplicial polytopes. We also apply this algebraic approach to obtain lower bounds on the numbers of vertices and edges of triangulations of manifolds and pseudomanifolds.

本文言語English
ページ(範囲)367-386
ページ数20
ジャーナルCollectanea Mathematica
66
3
DOI
出版ステータスPublished - 2015 9 18
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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