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# Questions tagged [differential-topology]

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”.

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### Separating two submanifolds [on hold]

Let $M, N, X$ are compact manifolds. Let $f_1:M \rightarrow X$ and $g_1: N \rightarrow X$ be any two embeddings. Is it always possible to find embeddings $f_2$ homotopic to $f_1$ and $g_2$ homotopic ...
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### Smooth structure for probability measures on separable Hilbert space

If $H$ is a separable Hilbert space (say, $L^2(\mathbb{R}^d)$ for concreteness), then it is well-known that the unit sphere $S$ of $H$ is a Hilbert manifold modeled on $H$ itself. The coordinate ...
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Consider $(\mathbb{C}P^2,\omega_{FS})$ where $\omega_{FS}$ is the standard Fubini-Study form. Let $L$ denote a sphere in $\mathbb{C}P^2$ in the class $\mathbb{C}P^1$. Further let $\int_{L} \omega_{FS} ... 3answers 282 views ### Wildness of codimension 1 submanifolds of euclidean space This question arose out of this stack exchange post. I am wirting a thesis about the$s$-cobordism theorem and Siebenmann's work about end obstructions. Combined they give a quick proof of the ... 0answers 85 views ### The space of$k$differential forms as a Fréchet space Given a smooth manifold$M$, can define define seminorms on$\Gamma(U,\bigwedge^kT^{\ast}M)$for$U$a coordinate open set by the following:$p^{s}_L(u = \sum_{I}u_I dx_I) = \sup_{x \in M}\max_{|I|=p, ...

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