A generalized lower bound theorem for balanced manifolds

Martina Juhnke-Kubitzke, Satoshi Murai, Isabella Novik, Connor Sawaske

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A simplicial complex of dimension d- 1 is said to be balanced if its graph is d-colorable. Juhnke-Kubitzke and Murai proved an analogue of the generalized lower bound theorem for balanced simplicial polytopes. We establish a generalization of their result to balanced triangulations of closed homology manifolds and balanced triangulations of orientable homology manifolds with boundary under an additional assumption that all proper links of these triangulations have the weak Lefschetz property. As a corollary, we show that if Δ is an arbitrary balanced triangulation of any closed homology manifold of dimension d- 1 ≥ 3 , then 2h2(Δ)-(d-1)h1(Δ)≥4(d2)(β~1(Δ)-β~0(Δ)), thus verifying a conjecture by Klee and Novik. To prove these results we develop the theory of flag h′ ′-vectors.

Original languageEnglish
Pages (from-to)921-942
Number of pages22
JournalMathematische Zeitschrift
Volume289
Issue number3-4
DOIs
Publication statusPublished - 2018 Aug 1

ASJC Scopus subject areas

  • Mathematics(all)

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