William Gollinger, University of Waterloo
"Four" proofs that \pi_1(G) is abelian
If G is a topological group then its fundamental group is abelian, which is usually not true for spaces. It is elementary to write down a homotopy that commutes any two elements, but where is the Fun in that? This talk also presents three "other" proofs in increasing degrees of abstraction, using functoriality of \pi_1, the Eckmann-Hilton trick, and the theory of group objects. All of the proofs will boil down to the same essential idea manifested in different contexts. Familiarity with algebraic topology and category theory are not necessary but never hurt.