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International Seminar for Young Researchers "Algebraic, Combinatorial and Toric Topology"
December 18, 2020 17:00–17:40, online

One-relator loop homology algebras of moment-angle complexes

G. Simmons

University of Southampton
 Video records: MP4 198.2 Mb

Abstract: For a flag complex $K$, we give a necessary and sufficient combinatorial condition for the loop homology algebra of the moment-angle complex $\mathcal Z_K$ to be a one-relator algebra. The condition we specify also characterises when the commutator subgroup of the right-angled Coxeter group corresponding to $K$ is a one-relator group, providing a combinatorial link between distinct concepts of geometric group theory and homotopy theory. Returning to moment-angle complexes, we give other equivalent algebraic and homotopy-theoretic formulations of our condition. In the non-flag case, many of these equivalences no longer hold, and we will present some of the key differences.