Geometry & Geometric Analysis Seminar
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and other campuses to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.
Title: Artin groups via mapping class groups
Abstract:
Artin groups are an important generalization of braid groups, occurring naturally
in topology, algebraic geometry and the theory of singularities. There is a subclass
of Artin groups for which methods involving mapping class groups and combinatorics
of curves on surfaces proved very fruitful and yielded interesting results. These
are the Artin groups which admit geometric embeddings into mapping class groups of
orientable surfaces, possibly, with punctures and/or boundary. In a series of recent
papers, in co-authorship with Paris, Calvez and Vaskou, we obtained new results for
these groups, such as a description of auto- and endomorphisms, investigating $R_\infty$
property, and the problem of classification up to commensurability. I will overview
these results, and describe some open problems which may be amenable to existing methods.