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... 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)
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