List questions from manifolds

Published on 13 Apr 2026 - 4:47

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$3$-manifold has same homology groups as a $3$-sphere.

Published on 07 Apr 2026 - 17:57

234

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Schubert Cells of Flags

Published on 31 Mar 2026 - 21:29

33

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is this map invertible?

Published on 12 Apr 2026 - 4:54

1.5k

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$f_: H_(S^n, \mathbb{Z}_p) \to H_*(M, \mathbb{Z}_p)$ an isomorphism if $p$ is a prime that does not divide $q$.

Published on 12 Apr 2026 - 21:19

113

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Multiplication by $q$ annihilates $H_i(M, \mathbb{Z})$ if $1 \le i \le n - 1$?

Published on 15 Apr 2026 - 2:09

370

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If $M$ is a nonorientable $3$-manifold, why is $H_1(M, \mathbb{Z})$ infinite?

Published on 25 Apr 2026 - 17:51

292

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Does it follow that $Y$ is homotopy equivalent to $S^{n-1}$?

Published on 03 Apr 2026 - 1:54

431

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Schubert cell decomposition and full flags

Published on 01 Apr 2026 - 18:56

626

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Top Cohomology group of a "punctured" manifold is zero?

Published on 16 Apr 2026 - 13:13

1.1k

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Higher math and statistics/probability

Published on 09 Apr 2026 - 10:56

75

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Is any of these two groups a smooth manifold?

Published on 28 Apr 2026 - 16:31

41

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Find a $C^∞$ map which is a one-one onto, inverse is continous but not a diffeomorphism.

Published on 16 Apr 2026 - 2:28

563

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Components in the complement of compact subset in manifold

Published on 11 Apr 2026 - 13:46

23

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Show $\varphi(x_1,...,x_{n+1})=\frac{1}{1-x_{n+1}}(x_1,...,x_n)$ is surjective.

Published on 17 Apr 2026 - 14:48

List Question

Dimension of homology of boundary is twice the dimension of kernel induced by inclusion.

$3$-manifold has same homology groups as a $3$-sphere.

Schubert Cells of Flags

is this map invertible?

$f_: H_(S^n, \mathbb{Z}_p) \to H_*(M, \mathbb{Z}_p)$ an isomorphism if $p$ is a prime that does not divide $q$.

Multiplication by $q$ annihilates $H_i(M, \mathbb{Z})$ if $1 \le i \le n - 1$?

If $M$ is a nonorientable $3$-manifold, why is $H_1(M, \mathbb{Z})$ infinite?

Does it follow that $Y$ is homotopy equivalent to $S^{n-1}$?

Schubert cell decomposition and full flags

Top Cohomology group of a "punctured" manifold is zero?

Higher math and statistics/probability

Is any of these two groups a smooth manifold?

Find a $C^∞$ map which is a one-one onto, inverse is continous but not a diffeomorphism.

Components in the complement of compact subset in manifold

Show $\varphi(x_1,...,x_{n+1})=\frac{1}{1-x_{n+1}}(x_1,...,x_n)$ is surjective.

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