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International Seminar for Young Researchers "Algebraic, Combinatorial and Toric Topology"
December 18, 2020 17:50–18:30, online

Duality in Toric Topology

M. Staniforth

University of Southampton
 Video records: MP4 181.2 Mb

Abstract: There are numerous notions of duality across mathematics. In this talk we explore the interplay between dualities in combinatorics, topology, and algebra, via a study of cup and cap products in moment-angle complexes and related polyhedral product spaces. We obtain both a description of the cap product and a characterisation of Poincaré duality in $\mathcal Z_K$, in terms of the combinatorics of the simplicial complex $K$. We then show how these results can be extended to a broader class of polyhedral products via simplicial substitution, and give a similar combinatorial characterisation of duality in such spaces.