List questions from homotopy-theory

Published on 14 Apr 2026 - 11:29

33

Views

Show that the identity $i:\mathbb{R}P^1 \longrightarrow \mathbb{R}P^1$ can not be lifted.

Published on 14 Apr 2026 - 2:56

184

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Understanding a step in example 4.34 in Hatcher.

Published on 17 Apr 2026 - 2:08

110

Views

Homotopy between $O(p,q)$ and $O(p)\times O(q)$

Published on 16 Apr 2026 - 5:06

508

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pointed homotopy equivalence

Published on 14 Apr 2026 - 6:20

415

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How to prove that the center of the fundamental group of $T_g$ is trivial for $g \geq 2$?

Published on 15 Apr 2026 - 17:48

748

Views

Pullback of fibration and homotopy equivalence

Published on 12 Apr 2026 - 5:28

106

Views

Any functor F equipped with a natural weak equivalence to or from the identity functor is homotopical by the 2-of-3 property.

Published on 16 Apr 2026 - 22:29

463

Views

Does the homotopy equivalence of a space with its subspace imply deformation retract?

Published on 12 Apr 2026 - 0:00

2.6k

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Definitions of free and based homotopy.

Published on 17 Apr 2026 - 22:16

857

Views

Homotopic equivalence embedding and contractible quotient space

Published on 14 Apr 2026 - 7:00

676

Views

homotopy and induced homomorphism.

Published on 12 Apr 2026 - 1:16

76

Views

Can $H_n(A) \cong H_n(X)$, where $(X,A)$ is a simply-connected $CW$ pair, always be induced by the inclusion map?

Published on 12 Apr 2026 - 15:16

78

Views

Isomorphism of higher homotopy groups

Published on 10 Apr 2026 - 23:03

994

Views

Pullback of homotopy equivalence along fibration is homotopy equivalence

Published on 13 Apr 2026 - 9:52

List Question

Milnor basis of Steenrod Algebra

Show that the identity $i:\mathbb{R}P^1 \longrightarrow \mathbb{R}P^1$ can not be lifted.

Understanding a step in example 4.34 in Hatcher.

Homotopy between $O(p,q)$ and $O(p)\times O(q)$

pointed homotopy equivalence

How to prove that the center of the fundamental group of $T_g$ is trivial for $g \geq 2$?

Pullback of fibration and homotopy equivalence

Any functor F equipped with a natural weak equivalence to or from the identity functor is homotopical by the 2-of-3 property.

Does the homotopy equivalence of a space with its subspace imply deformation retract?

Definitions of free and based homotopy.

Homotopic equivalence embedding and contractible quotient space

homotopy and induced homomorphism.

Can $H_n(A) \cong H_n(X)$, where $(X,A)$ is a simply-connected $CW$ pair, always be induced by the inclusion map?

Isomorphism of higher homotopy groups

Pullback of homotopy equivalence along fibration is homotopy equivalence

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