List questions from algebraic-topology | MathQA

Suppose $X$ is a contractible space and $A \subset X$ with $A$ being homotopy equivalent to $S^2$. Prove that there is no retraction $X \rightarrow A$

Published on 15 Apr 2026 - 19:49

Equivalence between the Dwyer-Kan loop groupoid and the fundamental groupoid

Published on 24 Mar 2026 - 22:09

Serre classes and the Serre spectral sequence

Published on 15 Apr 2026 - 2:10

Fundamental group of the real projective plane and its universal cover

Published on 12 Apr 2026 - 4:58

Equivalences of pairs are stable under pullback?

Published on 11 Apr 2026 - 21:29

$p:\widetilde{G} \rightarrow G$ a covering homomorphism, $\widetilde{H},H$ closed subgroups. Induced map on coset spaces is covering map.

Published on 12 Apr 2026 - 11:29

The fundamental group of the gluing of two genus $g$ $3$-dimensional handlebodies

Published on 13 Apr 2026 - 4:59

Can Fiber Bundles be seen as Exact Sequences?

Published on 10 Apr 2026 - 7:39

On construction of double cover of $\mathbb{R}P^{m}$

Published on 17 Apr 2026 - 3:36

Homology of the simplicial complex generated by all the faces of a fixed dimension

Published on 13 Apr 2026 - 19:36

group homomorphism $\Phi: \pi_1(X,x_0)^{ab}\to H_1(X,\mathbb{Z})$ where $\pi_1(X,x_0)^{ab}$ is the abelianization of the group $\pi_1(X,x_0)$.

Published on 14 Apr 2026 - 23:02

Is $\mathbb{CP}^4 \vee S^5$ homotopy equivalent to any compact manifold without boundary?

Published on 14 Apr 2026 - 9:31

Hatcher's proof of Poincare Duality

Published on 09 Apr 2026 - 6:10

$R$ orientation in Hatchers

Published on 10 Apr 2026 - 11:18

Constructing abelian group from commutative monoid.

Published on 12 Apr 2026 - 1:19