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Results tagged with surfaces
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user 172285
A surface is a two-dimensional topological manifold. The term can also be used to describe a smooth surface, depending on the context.
2
votes
1
answer
272
views
Lifting of a proper map in the cover is a proper map
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 b …
- 265
8
votes
2
answers
257
views
Degree one self-map of $\Bbb R^2\big\backslash \big\{(n,0):n\in \Bbb Z\big\}$ not homotopic ...
Consider the surface $\Sigma=\Bbb R^2\big\backslash \big\{(n,0):n\in \Bbb Z\big\}$. Does there exist a proper
map $f\colon \Sigma\to \Sigma$ of degree $1$ and not homotopic to
any self-homotopy equiv …
- 265