On face numbers of flag simplicial complexes
Yury Ustinovskiy

TL;DR
This paper revisits previous results on the homotopy groups and Poincaré series of moment-angle complexes associated with flag simplicial complexes, interpreting them as bounds on face numbers of such complexes.
Contribution
It provides a new interpretation of existing homotopy and Poincaré results as polynomial bounds on face numbers of flag simplicial complexes.
Findings
Homotopy group ranks and Poincaré series can be bounded polynomially
Reinterpretation of known results as face number bounds
Insights into face number limitations for flag complexes
Abstract
Denham, Suciu and Panov, Ray computed ranks of homotopy groups and Poincar\'e series of a moment-angle-complex ) / Davis-Januzskiewicz space associated to a flag simplicial complex . In this note we revisit these results and interpret them as polynomial bounds on the face numbers of an arbitrary simplicial flag complex.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models
