[Binghamton Geometry Topology Seminar] This week: Jacob Russell-Madonia

[jwilliams at math.binghamton.edu]

This week we will meet as usual on Thursday, May 9 at 2:50pm in WH 100E.

Speaker: Jacob Russell-Madonia (CUNY)

Title: The geometry of subgroup combination theorems

Abstract: 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
which 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 a large class of groups
demonstrate a similar local to global property from which an analogy of
Gitik's result can be obtained. This allows for a generalization of
Gitik's theorem in many important classes of groups including CAT(0)
groups, the mapping class groups of a surface, and 3-manifold groups.
Joint work with Davide Spriano and Hung C. Tran.