From: hook@nas.nasa.gov (Ed Hook) Subject: Re: fundamental group of topological group Date: 14 Jul 2000 15:24:27 GMT Newsgroups: sci.math Summary: [missing] In article <8kmp21$11pu3@hkunae.hku.hk>, Siu Lok Shun writes: |> I want for some exaample of non-abelian fundamental group. Take a "bouquet" of n circles, for n > 1. The fundamental group of this space is the free group on n generators. |> Is it ture that every fundamental group of topological groups are abelian? Yes. If X is a topological group and f, g: (S^1,1) --> (X,e) are loops at e, you can write down explicit homotopies between the loops f*g and g*f, using the group structure on X. (Here, '*' denotes the operation on paths that induces the multiplication in \pi_1.) -- Ed Hook | Copula eam, se non posit Computer Sciences Corporation | acceptera jocularum. NAS, NASA Ames Research Center | All opinions herein expressed are Internet: hook@nas.nasa.gov | mine alone