https://rochester.zoom.us/j/6775967436

To a group G and a family of subgroups F, one can associate a simplicial complex C(F,G), whose simplices are in correspondence with the chains of cosets of G with respect to the family. H. Abels and S. Holz studied homotopy properties of C(F,G), and their relationship with G. For example, C(F,G) is simply-connected if and only if G is the amalgamated product of subgroups in F along its intersections. C. Okay noted that for an arbitrary group G, specializing the simple-connectivity of C(F,G) to the family of abelian subgroups forces G to be abelian.

In this talk I will discuss a Lie group analogue of C(F,G) with respect to the family of abelian subgroups, arising from the work of Adem, Cohen and Torres-Giese. The main result I will describe is recent work with O. Antolín-Camarena and S. Gritschacher which deals with the analogue of Okay’s result for compact Lie groups.