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Results tagged with manifolds
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user 20787
A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
40
votes
Accepted
Connected sum of topological manifolds
In the topological category the proof that connected sum is well-defined depends on the Annulus Theorem, first proved by Kirby; the necessity of the Annulus Theorem is seen from Bruno Martelli's answe …
- 15.4k
10
votes
Self-covering spaces
Adding further counter-examples to the discussion, compact hyperbolic manifolds in all dimensions are ruled out by the fact that Gromov's "simplicial volume" is nonzero (being proportional to hyperbolic …
- 15.4k