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On Face Numbers of Flag Simplicial Complexes

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Denham and Suciu (Pure Appl Math Q 3(1):25–60, 2007) and Panov and Ray (in: Harada, et al. (eds) Toric topology. Contemporary Mathematics, American Mathematical Society, Providence, 2008) computed the ranks of homotopy groups and the Poincaré series of a moment-angle-complex \(\mathcal Z(\mathcal K\))/Davis–Januszkiewicz space \(DJ(\mathcal K)\) associated to a flag simplicial complex \(\mathcal K.\) 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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Acknowledgements

I am grateful to Taras Panov for fruitful discussions and many useful remarks. I would like also to thank anonymous reviewers for valuable comments, which helped improving this article.

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  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544-1000, USA

    Yury Ustinovskiy

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  1. Yury Ustinovskiy
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Correspondence to Yury Ustinovskiy.

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Ustinovskiy, Y. On Face Numbers of Flag Simplicial Complexes. Discrete Comput Geom 60, 688–697 (2018). https://doi.org/10.1007/s00454-018-9967-2

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  • DOI: https://doi.org/10.1007/s00454-018-9967-2

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