April 17, 2025
1:50 pm
-
2:50 pm
JR0387
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2025-04-17 13:50:00
2025-04-17 14:50:00
Topology Seminar - Michael Dougherty
Michael DoughertyLafayette CollegeTitleCell Structures for Braid Groups from Complex PolynomialsAbstractIn this talk, I will describe a new geometric and combinatorial structure for the space of complex polynomials with a fixed number of roots. In particular, I will define a metric on the space of monic polynomials with d distinct centered roots, and I will introduce 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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2025-04-17 13:50:00
2025-04-17 14:50:00
Topology Seminar - Michael Dougherty
Michael DoughertyLafayette CollegeTitleCell Structures for Braid Groups from Complex PolynomialsAbstractIn this talk, I will describe a new geometric and combinatorial structure for the space of complex polynomials with a fixed number of roots. In particular, I will define a metric on the space of monic polynomials with d distinct centered roots, and I will introduce 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.
JR0387
America/New_York
public
Michael Dougherty
Lafayette College
Title
Cell Structures for Braid Groups from Complex Polynomials
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. In particular, I will define a metric on the space of monic polynomials with d distinct centered roots, and I will introduce 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.
