Subject: Question about fundamental groups of topological groups From: Masoud Date: Mon, 26 Feb 2007 23:07:00 -0600 Let G be a connected topological group. Is the following complex exact? \pi_1(G\times G) ----> \pi_1([G,G])---->\pi_1(G) Here all the fundamental groups have as their base points the identity elements of the respective groups. The first map is induced by the commutator map (g,h) \mapsto ghg^{-1}h^{-1}, the second map is induced by the natural inclusion. Warning: The commutator map is not a group morphism. Thank you, Masoud Graduate Student University of Chicago