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Results tagged with smooth-manifolds
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user 50754
Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
2
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0
answers
35
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Immersions coming from projecting away from a line
Let $M$ be a compact $n$-manifold embedded in $\Bbb R^{2n}$ with $n \ne 1$. There is a map $F:S(TM) \to \Bbb RP^{2n-1}$ by identifying $TM$ as a subspace of of $\Bbb R^{2n}$ under the embedding. It is …
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3
votes
Is $TS^n$ diffeomorphic to an open subset of $\mathbb{R}^{2n}$
There are no sphere's with non-trivial normal bundle in that dimension. As far as I know, this is originally a theorem of Massey. See http://www.ams.org/journals/proc/1959-010-06/S0002-9939-1959-0109 …
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5
votes
Existence of tubular neighborohoods of locally flat topological embeddings
Assuming you mean $\pi$ is a closed disk bundle, I think a counterexample is given in the paper that first (as far as I know) constructed open disk bundles without closed disk sub-bundles. If you see …
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