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Results tagged with dg.differential-geometry
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user 22002
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
8
votes
1
answer
2k
views
Why is the Tangent Groupoid useful in non-commutative geometry?
Let $M$ be a smooth manifold. The classical construction is the tangent bundle $TM$. What does the tangent groupoid $GM$ give me that this construction doesn't, and why is it useful in non-commutative …
- 2,083
24
votes
2
answers
6k
views
Are Banach Manifolds intrinsically interesting?
In the introduction to 'A convenient setting for Global Analysis', Michor & Kriegl make this claim: "The study of Banach manifolds per se is not very interesting, since they turnout to be open subsets …
- 2,083
1
vote
1
answer
212
views
gluing bundles as a 2-colimit
Is the gluing of bundles from not-necessarily trivial bundles just some kind of 2-colimit?
- 2,083
1
vote
Accepted
gluing bundles as a 2-colimit
not my answer, but David Carchedi's answer in a comment:
'What you might be thinking is, the category of principal bundles over a fixed base is a 2-colimit over all covers of the base (or some cofina …
- 2,083
13
votes
3
answers
2k
views
What is the characteristic property of surjective submersions?
In Lee's Introduction to smooth manifolds he states that given smooth manifolds $X,Y$ and a surjective submersion, $f:X \rightarrow Y$, then $f$ is a smoothly final map, that is for any further smooth …
- 2,083