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A relatively clean and intuitive proof is given in Kosinski's "Differential Manifolds," which works in the topological setting and essentially boils down to the following: If $M$ is path-connected an …

Let $\Theta_n$ be the set of orientation-preserving diffeomorphism classes of homotopy spheres, with abelian group structure given by #. Then for any smooth manifold $M^n$ one defines the "inertia su …

See Smooth manifold with non-trivial inertia group? (wrt homotopy spheres) for the definition of $\Theta_n$ and inertia subgroups. I'm wondering what can be said about Lie groups. If $M^n$ is an n-d …

Say that $S^n$ "admits eversion" if the inclusion $S^n \rightarrow \mathbb{R}^{n+1}$ is regularly homotopic to the antipodal map (where a "regular" homotopy is a continuous path through immersions). …

I will phrase this question in terms of attaching smooth manifolds along a submanifold, though it is certainly more general. Let $M_1$ and $M_2$ be smooth $n$-manifolds (maybe closed, for simplicity) …

Smooth (closed, connected, orientable) 3-dimensional manifolds are very special, in that for any 3-manifold $M$ there are two handlebodies, $V$ and $W$, of genus $g$ and an orientation reversing homeo …

I think the statement of the question is pretty straightforward. Given a finite $n$-dimensional CW complex, are there necessary and sufficient conditions for determining that it is also a compact $n$ …