# Omar Antolín Camarena: Classifying spaces for commutativity in groups

**Time: **
Thu 2020-03-05 10.15 - 12.00

**Location: **
Kräftriket, house 6, room 306 (Cramér-rummet)

**Lecturer: **
Omar Antolín Camarena, Instituto de Matemáticas, UNAM

### Abstract

Given a topological group G, we can think of the space of homomorphisms \(\hom(\mathbb{Z}^n, G)\) as the space of \(n\)-tuples of elements of \(G\) that commute pairwise. These spaces are more subtle than one might think, and even basic invariants such as the number of connected components can lead to surprising results. Fixing \(G\) and varying \(n\) we can construct what is known as the classifying space for commutativity in \(G\). I will survey what is known about these classifying spaces, whose study is still young.