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Let $M$ be an orientable surface without boundary$($I am not assuming $M$ is compact, it can be non-compact$)$. Let $\Phi: M\to M$ be a proper homotopy-equivalnce$($A proper homotopy-equivalence can ...

Question. Let $M$ be a triangulated non-orientable 3-manifold with non-orientable boundary. (It is possible to assume that the boundary is the Klein bottle.) Let $\ell$ be a non-orientable loop on the ...

I am learning some things about surfaces of genus greater than $1$, and I am trying to answer this question : Let $S$ be a compact and orientable surface of genus $g \geq 2$, and $c$ a closed curve ...

We are interested in the following ´relative´ version of residual finiteness for fundamental groups of surfaces. Similar discussions where given in this question: injectivity radius of hyperbolic ...