Big mapping class groups and uniqueness of Polish structures

Abstract: Suppose you are given a topological group. You may wonder about how much the group structure determines the topology. At first glance, the answer appears to be "not very much at all", since every topological group admits the discrete topology, and the trivial topology, both of which are compatible with the group operation.

Mapping class groups of infinite-type surfaces are humungous (not a technical term), and come equipped with a Polish topology. We can ask a refinement of the above question: How much does the group structure of a mapping class group determine its Polish topology? In this talk we'll investigate this question, leading to a perhaps surprising answer.

This is joint work with Sumun Iyer, Robbie Lyman, and Nick Vlamis.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

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CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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