All Questions
Tagged with cotangent-bundles vector-bundles
7 questions
2
votes
1
answer
123
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Normal bundle of veronese as iteration extension of symmetric powers
In this post, an answer claims that the normal bundle of the Veronese decomposes into a filtration, such that the associated graded is $$\bigoplus_{i=2}^d S^i T,$$ where $T$ is the tangent bundle. But ...
- 129
8
votes
1
answer
806
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Derivations on the continuous functions of a manifold
For a manifold $M$ a vector field is a derivation of the algebra $C^{\infty}(M)$ of smooth functions on $M$. What happens if look instead as derivations on the continuous functions of a manifold. I ...
- 969
0
votes
0
answers
161
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Projectivization of the normal bundle of $\mathbb P^4$ in the 10-spinor variety
Let $X=S_{10} \subset \mathbb P^{15}$ be the 10-dimensional spinor variety in its minimal embedding. Consider a $\mathbb P^4 \subset S_{10}$, hence we can define the normal bundle $N=N_{\mathbb P^4|S_{...
- 381
4
votes
1
answer
356
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Natural extension homomorphism and wrong-way maps in K-theory
Let $X \subset Y$ be two smooth manifolds. To the inclusion $I:X \to Y$ corresponds the so called wrong-way map in $K-theory$ $i_!:K(X) \to K(Y)$. It is constructed as follows: to the inclusion $X \...
- 9,340
14
votes
3
answers
2k
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Splitting of tangent bundle
Is it possible to give an example of $n$ dimensional manifold with the property that the tangent bundle $TM$ cannot be expressed as Whitney sum of two subbundles? It is certain true for two sphere; it ...
- 9,340
3
votes
1
answer
221
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A question on long line
Assume that $M$ is the long line. Is $TM$, the tangent bundle, isomorphic to $T^{*}(M)$, the cotangent bundle?
- 366
1
vote
1
answer
493
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Is there a relationship between tensor (or form) bundles and iterated tangent/cotangent bundles on a manifold?
Let's say we denote by $T^{(n,m)}M$ the vector-bundle of rank $(n,m)$ tensors on a manifold $M$ and by $\Lambda^pM$ the vector-bundle of $p$-forms on $M$. Is there a relationship (perhaps a ...
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