What is... an infinite loop space?

Markus Hausmann will explain what infinite loop spaces are.

Abstract: Given a topological space X with a chosen basepoint, one can consider its loop space whose elements are given by the paths in X that start and end at the basepoint. Given two such loops, one can form a third loop by concatenation, giving the loop space a continuous multiplication.  In the talk I will explain in what sense forming iterated loop spaces makes this multiplication more and more commutative and why the limit, so-called infinite loop spaces, are the homotopy-theoretic analog of abelian groups. These objects play a central role in algebraic topology and I will try to illustrate why.

"What is...?" is an accessible and non-technical seminar where speakers explain in one (short) lecture some object or theorem that they think is interesting. There will be drinks and snacks during the talk. See the seminar website for more information.