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A Tale of Centrally Symmetric Polytopes and Spheres

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Recent Trends in Algebraic Combinatorics

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 16))

Abstract

This paper is a survey of recent advances as well as open problems in the study of face numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed range from neighborliness of centrally symmetric polytopes and the Upper Bound Theorem for centrally symmetric simplicial spheres to the Generalized Lower Bound Theorem for centrally symmetric simplicial polytopes and the lower bound conjecture for centrally symmetric simplicial spheres and manifolds.

Research is partially supported by NSF grants DMS-1361423 and DMS-1664865, and by Robert R. and Elaine F. Phelps Professorship in Mathematics. This material is based on work supported by the National Science Foundation under Grant No. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley CA, during the Fall 2017 semester.

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Acknowledgements

I am grateful to Steve Klee, Connor Sawaske, Hailun Zheng, Günter Ziegler, and the anonymous referee for numerous comments on the preliminary version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195-4350, USA

    Isabella Novik

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  1. Isabella Novik
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Correspondence to Isabella Novik .

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  1. Mathematical Sciences Research Institute , Berkeley, CA, USA

    Hélène Barcelo

  2. Department of Mathematics, Pomona College, Claremont, CA, USA

    Gizem Karaali

  3. Department of Mathematics, Dartmouth College, Hanover, NH, USA

    Rosa Orellana

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Novik, I. (2019). A Tale of Centrally Symmetric Polytopes and Spheres. In: Barcelo, H., Karaali, G., Orellana, R. (eds) Recent Trends in Algebraic Combinatorics. Association for Women in Mathematics Series, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-030-05141-9_9

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