Stellar theory for flag complexes

Frank H. Lutz, Eran Nevo

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Refining a basic result of Alexander, we show that two flag simplicial complexes are piecewise linearly homeomorphic if and only if they can be connected by a sequence of flag complexes, each obtained from the previous one by either an edge subdivision or its inverse. For flag spheres we pose new conjectures on their combinatorial structure forced by their face numbers, analogous to the extremal examples in the upper and lower bound theorems for simplicial spheres. Furthermore, we show that our algorithm to test the conjectures searches through the entire space of flag PL spheres of any given dimension.

Original languageEnglish
Pages (from-to)70-82
Number of pages13
JournalMathematica Scandinavica
Volume118
Issue number1
DOIs
StatePublished - 1 Jan 2016

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