The geometry of subgroup combination theorems

Geometry Topology Seminar
Monday, October 21, 2019 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Jacob Russell – CUNY Graduate Center – jrussellmadonia@gradcenter.cuny.edu
Justin Lanier

While producing subgroups of a group by specifying generators is easy, understanding  the structure of such a subgroup is notoriously difficult problem.  In the case of hyperbolic groups, Gitik utilized a local-to-global property for geodesics to produce an elegant condition that ensures a subgroup generated by two elements (or more generally generated by two subgroups) will split as an amalgamated free product over the intersection of the generators. We show that the mapping class group of a surface and many other important groups have a similar local-to-global property from which an analogy of Gitik's result can be obtained.   In the case of the mapping class group, this produces a combination theorem for the dynamically and topologically important convex cocompact subgroups.  Joint work with Davide Spriano and Hung C. Tran.