Re: iterating the fundamental groupoid does not work, so.....

[David Roberts <droberts@maths.adelaide.edu.au>]

On 29 April 2010 05:48, Ronnie Brown <ronnie.profbrown@btinternet.com>wrote:

> I would like to make a further point about the topological fundamental
> groupoid of X.  The information on this shows that iterating the
> fundamental groupoid does NOT lead to higher dimensional information on X.
>
>
If this means what I think it means: applying Pi_1 to the arrows and objects
of the topologised fundamental groupoid, then I agree. In a suitable
bicategory of topological groupoids (where internal weak equivalences a la
Bunge-Pare or Everaert-Kieboom***-*van der Linden are formally inverted) the
topologised fundamental groupoid is equivalent to a groupoid sans topology -
in fact it is equivalent to itself where the topology is replaced by the
discrete topology. The topologised fundamental groupoid in this way encodes
only the 1-type of the space.


David Roberts


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]