A generalized lower bound theorem for balanced manifolds

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

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Abstract

A simplicial complex of dimension (Formula presented.) 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 (Formula presented.) is an arbitrary balanced triangulation of any closed homology manifold of dimension (Formula presented.), then (Formula presented.), thus verifying a conjecture by Klee and Novik. To prove these results we develop the theory of flag (Formula presented.)-vectors.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalMathematische Zeitschrift
DOIs
Publication statusAccepted/In press - 2017 Nov 15
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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