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Results tagged with dg.differential-geometry
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user 75783
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
5
votes
Accepted
Intuition and analogue of Wraith axiom from synthetic differential geometry
Axiom W is about the behaviour of the second tangent bundle - it ensures that the vertical bundle of the tangent bundle, $V(M) \subseteq T\circ T(M)$, where $V(M) = T(p)^{-1}(0)$, decomposes as the pu …
- 1,253
6
votes
0
answers
293
views
Examples of connection preserving maps in differential geometry
In synthetic differential geometry and tangent categories, linear connections on the tangent bundle are treated as a sort of algebraic gadgets that incorporate the tangent bundle. Like any other algeb …
- 1,253
2
votes
1
answer
144
views
Identifying Lie groupoids among smooth groupoids
I have been approaching groupoids in the category of smooth manifolds using methods from essentially algebraic theories/limit sketches. Are there any results that identify Lie groupoids amongst intern …
- 1,253
2
votes
Identifying Lie groupoids among smooth groupoids
Well this is embarrassing, I asked this question after spending a weekend thinking about it staring at the definition all day and two hours later I have a partial answer - it seems that this is equiva …
- 1,253
2
votes
1
answer
116
views
Special cases of Lie II for groupoids using elementary techniques
I asked a similar question on math.stackexchange but did not get any responses, so I thought I'd kick it up to mathoverflow.
In Crainic and Fernandes's "Integrability of Lie Brackets" (and the accompa …
- 1,253
2
votes
1
answer
110
views
"Lie theory" for anchored bundles and reflexive graphs
Perhaps Lie theory is not the correct term, but I'm thinking of the intermediate result in the Lie groupoid to Lie algebroid correspondence. Given a Lie groupoid $G$ over $M$, we may construct the Lie …
- 1,253
2
votes
Geometric intuition for $R[x,y]/ (x^2,y^2)$, kinematic second tangent bundle, and Wraith axiom
I will try to address your questions, and then point to some general cartegorical phenomena that are at play here.
Answer 1/2: In the category of smooth manifolds, or a proper model of synthetic diffe …
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