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Results tagged with differential-topology
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user 21965
The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
9
votes
2
answers
2k
views
Transitivity of automorphism group of smooth manifolds
Suppose $M$ is a connected smooth manifold and $x,y \in M$ are two points. Is there always a
diffeomorphism $\phi: M \rightarrow M$ with $\phi(x)= y$ ?
- 2,074
2
votes
1
answer
311
views
Natural Transformations from the Tensor product of tangent bundle into the second order tang...
Short question with long title:
Suppose $T$ is the tangent functor and $T^2:=T\circ T$ is the second order tangent functor.
Are there natural transformations $T\otimes T \Rightarrow T^2$ ?
I consid …
- 2,074
2
votes
3
answers
677
views
Criteria for Involutive Subbundles
Preliminaries: Let $M$ be a smooth manifold with tangent bundle $TM$. A vector subbundle
$VM$ of $TM$ is called involutive if the section space $\Gamma(VM)$ of $VM$ is closed under
the Lie bracket o …
- 2,074
1
vote
1
answer
631
views
Pullbacks and Inclusions of Smooth function algebras of manifolds.
Let $M$ and $N$ be two smooth finite dimensional manifolds and
$C^\infty(M)$ as well as $C^\infty(N)$ their smooth function algebras.
Is the following true:
Let $\imath: M \to N$ be an embedding. Th …
- 2,074
9
votes
1
answer
2k
views
Differential Calculus and the De Rham Homotopy Operator
Suppose $M$ is a smooth manifold, $\Omega^k(M)$ the vector space (or $C^\infty(M)$-module in case this is better suited) of $k$-differentialforms on $M$ and
$$I: \Omega^k(M\times \mathbb{R}) \to \Ome …
- 2,074
5
votes
1
answer
346
views
Exercises around Diffeological Spaces or a Diffeologic Atlas Theory
Is there a Book or a bunch of exercises to get used to diffeological spaces from a practical point of view? It seems to me that papers on this topic are mostly concerned with their very good categoric …
- 2,074