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Results tagged with surfaces
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user 58307
A surface is a two-dimensional topological manifold. The term can also be used to describe a smooth surface, depending on the context.
4
votes
Group of surface homeomorphisms is locally path-connected
In the particular case of surfaces, I found the following reference which includes a proof that is not too complicated: Regular Mappings and the Space of Homeomorphisms on 2-Manifolds by Hamstrom and Dyer … It works for surfaces with or without boundaries and includes a slight generalization with fixed points on the boundary. This is Theorem 1 in this article. …
- 1,517
10
votes
2
answers
431
views
Group of surface homeomorphisms is locally path-connected
I think the following is true and I need a reference for the proof. (Given a closed surface $S$, i.e. a compact 2-dimensional topological manifold (without boundary), we endow $S$ with a distance gene …
- 1,517