Cihan Okay

Title: Commutative bundles and their applications

Abstract: Principal bundles with commutativity structure on their
transition functions are introduced by Adem and Gomez. These objects
are classified by the classifying space for commutativity which is a
variant of the ordinary classifying space of a topological group
assembled from pairwise commuting group elements. In this talk, based
on joint work with Pal Zsamboki, I will describe how to carry over
such constructions to the category of simplicial groups. This leads to
interesting variants of Kan's loop group functor and the bar
construction for simplicial groups. Moreover the geometric realization
functor relates the simplicial version to the topological
version. This way many interesting examples studied earlier can be
carried over to the simplicial category. Time permitting I will tell a
bit about applications to problems arising in quantum information
theory.