Cell Structures for Braid Groups from Complex Polynomials

Michael Dougherty (Lafayette College)

Monday 20th April 15:00-16:00
Maths 311B

Abstract

In this talk, I will describe a new geometric and combinatorial structure for the space of complex polynomials with a fixed number of roots. This structure comes from introducing an unusual metric on the space of monic polynomials with d distinct centered roots, then defining a finite cell structure for the metric completion. Each cell in this complex is a product of two Euclidean simplices, and the combinatorial structure comes from the dual presentation for the d-strand braid group. In particular, this provides a concrete connection between two classifying spaces for the braid group. This is joint work with Jon McCammond.

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