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Results tagged with at.algebraic-topology
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user 126010
Homotopy theory, homological algebra, algebraic treatments of manifolds.
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How many n-dimensional closed submanifolds of $R^n$ have Euler characteristic 1?
It is well-known that the closed $n$-ball has Euler characteristic $1$. Is it true that every closed (i.e., compact), connected $n$-dimensional submanifold (with boundary) of $\mathbb R^n$ having Eule …
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Do closed hypersurfaces separate the euclidean space?
The following extension of the Jordan Curve Theorem is well known: every closed connected hypersurface of the sphere $\mathbb S^N$ separates $S^N$ into exactly two connected components. As a consequen …