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Results tagged with manifolds
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user 259525
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.
7
votes
1
answer
341
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Decomposition of manifolds with toroidal boundary
Let $\mathcal{M}$ be a compact, connected, oriented 3-manifolds with non-empty connected boundary $\partial\mathcal{M}$. … So this is basically a generalization of the famous prime decomposition ("Kneser-Milnor theorem") to the case of manifolds with boundary. …
- 1,429
14
votes
1
answer
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Classification of 3-dimensional manifolds with boundary
It is well-known that every closed, connected and orientable 3-manifold $\mathcal{M}$ can uniquely be decomposed as
$$\mathcal{M}=P_{1}\#\dots\# P_{n}$$
where $P_{i}$ are prime manifolds, i.e. manifolds … which can not be written as a non-trivial connected sum of two 3-manifolds. …
- 1,429