Question

cohomology is dual to homology of a spectrum if homology is free

score 335 · Answer 1 · 2026-04-11 18:00:10

335

Views

cohomology is dual to homology of a spectrum if homology is free

Published on 11 Apr 2026 - 18:00

score 839 · Answer 2 · 2026-04-10 04:51:42

839

Views

Higher homotopy groups: Basepoint independence.

Published on 10 Apr 2026 - 4:51

score 522 · Answer 3 · 2026-04-15 03:00:48

522

Views

Loop space of $S^1$

Published on 15 Apr 2026 - 3:00

score 257 · Answer 4 · 2026-04-12 10:45:37

257

Views

Is the homotopy class given by the degree?

Published on 12 Apr 2026 - 10:45

score 1.7k · Answer 5 · 2026-04-13 00:25:42

1.7k

Views

Proof of the Borsuk-Ulam Theorem

Published on 13 Apr 2026 - 0:25

score 534 · Answer 6 · 2026-04-14 06:09:11

534

Views

Simple example of $X$ with torsion in $H^1(X,\mathbb{Z})$?

Published on 14 Apr 2026 - 6:09

score 78 · Answer 7 · 2026-04-16 08:56:15

78

Views

why does the flipping map $S^1 \wedge S^1 \to S^1 \wedge S^1$ introduce a minus sign in homotopy?

Published on 16 Apr 2026 - 8:56

score 707 · Answer 8 · 2026-04-08 12:45:44

707

Views

Extending a homeomorphism of the open disk to the boundary.

Published on 08 Apr 2026 - 12:45

score 594 · Answer 9 · 2026-04-15 22:21:12

594

Views

A curve not homotopic to constant path but index of every point is zero.

Published on 15 Apr 2026 - 22:21

score 295 · Answer 10 · 2026-04-14 18:32:06

295

Views

Does the $\Omega$-spectrum functor send exact triangles to homotopy cofiber sequences?

Published on 14 Apr 2026 - 18:32

score 781 · Answer 11 · 2026-04-14 11:26:08

781

Views

Homotopy direct limit versus direct limit

Published on 14 Apr 2026 - 11:26

score 278 · Answer 12 · 2026-04-16 15:31:29

$X$ is contained in an annulus containing a circle in the annulus.Show that $\pi_1(X)$ contains a subgroup isomorphic to $\mathbb{Z}$.

score 151 · Answer 13 · 2026-04-10 23:02:48

151

Views

Skeletality of a simplicial set $X$ vs. highest degree of a non-degenerate simplex

Published on 10 Apr 2026 - 23:02

score 1.9k · Answer 14 · 2026-04-16 02:46:29

1.9k

Views

prove that the identity map $i:S^n\to S^n$ is not nullhomotopic.

Published on 16 Apr 2026 - 2:46

score 102 · Answer 15 · 2026-04-13 13:39:16

102

Views

When may the bar resolution be truncated for calculating $\operatorname{hocolim}$?

Published on 13 Apr 2026 - 13:39

List Question

cohomology is dual to homology of a spectrum if homology is free

Higher homotopy groups: Basepoint independence.

Loop space of $S^1$

Is the homotopy class given by the degree?

Proof of the Borsuk-Ulam Theorem

Simple example of $X$ with torsion in $H^1(X,\mathbb{Z})$?

why does the flipping map $S^1 \wedge S^1 \to S^1 \wedge S^1$ introduce a minus sign in homotopy?

Extending a homeomorphism of the open disk to the boundary.

A curve not homotopic to constant path but index of every point is zero.

Does the $\Omega$-spectrum functor send exact triangles to homotopy cofiber sequences?

Homotopy direct limit versus direct limit

$X$ is contained in an annulus containing a circle in the annulus.Show that $\pi_1(X)$ contains a subgroup isomorphic to $\mathbb{Z}$.

Skeletality of a simplicial set $X$ vs. highest degree of a non-degenerate simplex

prove that the identity map $i:S^n\to S^n$ is not nullhomotopic.

When may the bar resolution be truncated for calculating $\operatorname{hocolim}$?

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