Squeezed complexes

Martina Juhnke-Kubitzke, Uwe Nagel

Research output: Contribution to journalArticlepeer-review

Abstract

Given a shifted order ideal (Formula presented.), we associate to it a family of simplicial complexes (Formula presented.) that we call squeezed complexes. In a special case, our construction gives squeezed balls that were defined and used by Kalai to show that there are many more simplicial spheres than boundaries of simplicial polytopes. We study combinatorial and algebraic properties of squeezed complexes. In particular, we show that they are vertex decomposable and characterize when they have the weak or the strong Lefschetz property. Moreover, we define a new combinatorial invariant of pure simplicial complexes, called the singularity index, that can be interpreted as a measure of how far a given simplicial complex is from being a manifold. In the case of squeezed complexes (Formula presented.), the singularity index turns out to be strictly decreasing until it reaches (and stays) zero if (Formula presented.) grows.

Original languageEnglish
Pages (from-to)110-135
Number of pages26
JournalJournal of the London Mathematical Society
Volume101
Issue number1
DOIs
StatePublished - Feb 1 2020

Bibliographical note

Publisher Copyright:
© 2019 London Mathematical Society

Keywords

  • 05E40
  • 13F55 (primary)

ASJC Scopus subject areas

  • Mathematics (all)

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