List questions from homotopy-theory

Published on 17 Apr 2026 - 5:48

266

Views

Homotopy Extension Property as a pushout?

Published on 11 Apr 2026 - 22:00

120

Views

Show that if $f:S^8 \to S^8$ and $\|f(x) + x\| < 1$ for all $x$ then $f$ is not homotopic to the identity map

Published on 15 Apr 2026 - 21:37

551

Views

Kan's loop group construction

Published on 08 Apr 2026 - 22:33

95

Views

Is the following true about maps on unit closed disc?

Published on 14 Apr 2026 - 0:33

351

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Lifting property of a covering map, product topology version

Published on 16 Apr 2026 - 11:22

258

Views

Criterion for a map to be homotopy equivalence in terms of its mapping cylinder

Published on 13 Apr 2026 - 4:37

75

Views

Weak equivalence testable on invariant open covers?

Published on 14 Apr 2026 - 21:10

1.4k

Views

Homotopy equivalence between O-O and $\theta$

Published on 13 Apr 2026 - 15:21

539

Views

Explicit construction of Eilenberg-Maclane spaces with n=1

Published on 26 Mar 2026 - 4:51

131

Views

what is the inclusion map for $Y$ to $Y$ x $Y$?

Published on 11 Apr 2026 - 11:39

100

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Show $X$ is a H-space?

Published on 11 Apr 2026 - 19:34

417

Views

Aspherical but not contractible

Published on 13 Apr 2026 - 3:09

1.1k

Views

Showing that identity and g are not homotopic (without Homology)

Published on 13 Apr 2026 - 23:50

5.5k

Views

Residue Theorem and Homologous to zero

Published on 12 Apr 2026 - 20:23

List Question

Utility of the 2-Categorical Structure of $\mathsf{Top}$?

Homotopy Extension Property as a pushout?

Show that if $f:S^8 \to S^8$ and $\|f(x) + x\| < 1$ for all $x$ then $f$ is not homotopic to the identity map

Kan's loop group construction

Is the following true about maps on unit closed disc?

Lifting property of a covering map, product topology version

Criterion for a map to be homotopy equivalence in terms of its mapping cylinder

Weak equivalence testable on invariant open covers?

Homotopy equivalence between O-O and $\theta$

Explicit construction of Eilenberg-Maclane spaces with n=1

what is the inclusion map for $Y$ to $Y$ x $Y$?

Show $X$ is a H-space?

Aspherical but not contractible

Showing that identity and g are not homotopic (without Homology)

Residue Theorem and Homologous to zero

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