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Results tagged with differential-topology
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user 16702
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”.
10
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0
answers
754
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Differential Forms in Infinite Dimensions
In Kriegl/Michor's book "The convenient setting of global analysis", they define the space of differential $k$-forms on a possibly infinite-dimensional manifold $M$ as the space of smooth sections of …
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5
votes
0
answers
82
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Vector bundles on space of germs
Let $X$ be the diffeological space of germs of paths $c: \mathbb{R} \rightarrow \mathbb{R}^n$, where two paths $c_1, c_2$ are equivalent if $c_1(t) = c_2(t)$ for all $t$ in some interval $(-\varepsilo …
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4
votes
Take contraction wrt a vector field twice and define kernel mod image. Does that give anythi...
I believe that the answer is something in between "not really" and "kind of" and was indicated by Qiaochu Yan.
In Wittens famous paper "Morse Theory and Supersymmetry", he considers operators of the …
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4
votes
1
answer
279
views
Isometry Group of real Hilbert space?
Does the isometry group of a real separable infinite-dimensional Hilbert space have two connected components? Or, conversely, is the there even a Kuiper's theorem in the real case?
How does the isome …
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3
votes
Does every vector bundle allow a finite trivialization cover?
I wonder that this was not said before.
Take a triangulation of your manifold. Choose disjoint open balls around each 0-cell in the triangulation and set the union to be $U_0$ (a ball means here some …
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3
votes
Calculation of the top Chern class of spinor bundle over $S^{2n}$
I will present an explicit calculation using Chern-Weil theory, which makes an amusing use of Legendre's duplication formula for the gamma function.
The Chern character form of a vector bundle $E$ wit …
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