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0 votes
2 answers
810 views

Why study orbifolds? [closed]

Why study orbifolds? I study orbifolds as locally compact Hausdorff spaces $X$ having an orbifold structure, i.e., there exists an orbifold groupoid (proper foliatio. … Edit : Wikipedia page does not say anything about groupoid way of looking at orbifolds. I did not mean to ask for references for orbifolds or groupoids. …
3 votes
1 answer
357 views

Proper and etale groupoid is locally a translation groupoid

I am reading Orbifolds as Groupoids: an Introduction by Ieke Moerdijk. In page $8$ when explaining local charts, it says the following : Let $\mathcal{G}$ be a Lie groupoid. … Reference given is Orbifolds, Sheaves and Groupoids by Ieke Moerdijk and D. A. Pronk. …
3 votes
2 answers
313 views

Necessity/Motivation for generalised homomorpisms

I am reading Ieke Moerdijk's article "Orbifolds as Groupoids : an Introduction". In that notes author defines a notion of generalized map between Lie groupoids. …
1 vote
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210 views

Idea behind definition of classifying space over an orbifold

Today I was explaining to some one the notion of $\mathcal{G}$ spaces, covering spaces over orbifolds from Orbifolds as Groupoids: an Introduction. … Orbifolds are something more than just a topological space and less than a smooth manifold. …