Remark on: Re: gr-stacks (revised)

Remark on: Re: gr-stacks (revised)

[Ronnie Brown]

David,

When you have `bad' quotients you can look at the equivalence relation, a
special case of a groupoid. In the case of subgroups H < G, then you also
get a covering groupoid G' \to G with vertex groups isomorphic to H.  If you
want more than one subgroup, you might need global actions or groupoid
atlases

http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/06/algtop06.html#06.02

Perhaps you can find `bad' quotients which nonetheless have `good' holonomy
groupoids, analogously to the foliation case? That would be good, but is it
too naive an idea? On the other hand, an irrational flow on a torus gives a
foliation of the torus which has a smooth holonomy groupoid.

see preprint 06.03  and the information there for some ideas on holonomy.

Ronnie Brown

----- Original Message -----
From: "David Roberts" <d.roberts@student.adelaide.edu.au>
To: <categories@mta.ca>
Sent: Saturday, May 06, 2006 5:09 AM
Subject: categories: gr-stacks (revised)


> Categorists,
>
>
> On Sat, Apr 29, 2006 at 01:27:20PM +0930, David Roberts wrote:
>
>> Dear all,
>>
>> after a bit of searching, I cannot find much in the literature about gr-
>> stacks, more specifically, charts and presentations thereof reflecting
>> (in a
>> non-technical sense) the group-like structure. Also, aside from self
>> equivalences of gerbes and quotients of groups **(G/H for non-normal
>> H)**, I
>> cannot dream up other "interesting" examples - and these are the opposite
> ends
>> of the spectrum I want to consider.
>
>
> A bit of confusion occured when I tried to post a corrected version of the
> above (all due to myself), so here goes.
>
> I retract the statement in ** ** above - what I meant was G/H with a badly
> behaved topological/differentiable quotient (H normal in G) and I was
> after
> examples not connected with gerbes/crossed modules but something more
> `interesting' than group quotients.
>
> Thanks,
>
> --
> David Roberts
> Pure Mathematics
> University of Adelaide
> South Australia, 5005
>
> You know we all became mathematicians for the same reason: we were lazy.
> -Max Rosenlicht(1949)
>
>
>