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Homotopy theory, homological algebra, algebraic treatments of manifolds.

1 vote
0 answers
130 views

A question about a manifold in an $n$-dimensional Alexandrov space with curvature bounded below [duplicate]

Suppose $M$ is an $n$-dimensional Alexandrov space with curvature bounded below(maybe with boundary), subspace $A\subset M$ is an $n$-dimensional manifold without boundary. Then whether every point in …
Lewis Zhang's user avatar
1 vote
1 answer
428 views

Does the singular cohomology for a metric space of finite topological dimension vanish in hi...

It is known that by applying the universal coefficient theorem, the singular cohomology of closed manifold with coefficient $\mathbb{Z}_2$ vanishes in high dimensions. But for a metric space $M$ with …
Lewis Zhang's user avatar