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This got 5 upvotes but no answers on MSE (Mapping torus of Klein bottle), so I'm cross-posting to MO: The mapping torus of a Klein bottle $ K $ is a compact flat 3 manifold. The mapping class group of ...

Recently, A. Carlotto and C. Li proved a complete topological classification of those compact, connected and orientable $3$-manifolds with boundary which support Riemannian metrics of positive scalar ...

Let $M$ be a $C^{\infty}$-smooth, connected, paracompact manifold with universal cover $\tilde{M}$. Assume $M$ is not simply connected, so that the covering map $p : \tilde{M} \to M$ is not the ...

I also posted this question on MSE, but since it may be a delicate question, I decided to post it here. Given a Riemannian manifold $(M^n,g)$ and an integer $1 \leq k \leq n-1$, the $k$-systole of $M$ ...