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 <lssiu@hkusua.hku.hk> 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