New posts in algebraic-topology

Fundamental group is abelian iff the fundamental group isomorphisms (a-hat) coincide

Equivalent definition $\text{Cone}(K)$

What are the ramifications of the fact that the first homotopy group can be non-commutative, whilst the higher homotopy groups can't be?

Spin manifold and the second Stiefel-Whitney class

For every $k \in {\mathbb Z}$ construct a continuous map $f: S^n \to S^n$ with $\deg(f) = k$.

Why is the Long Line not a covering space for the Circle

Topological properties that aren't conserved over homotopy?

What are cohomology rings good for?

Euler characteristic of $\mathbb{R}$ and $\mathbb{R}^2$?

For a graph $(G, V)$, $\# \text{edges}$ is given by the rank of $H_1(G, V)$.

Problem handling free groups in algebraic topology

Homotopy type of the complement of a subspace

Is a finite dimensional CW complex with the same homotopy groups as $S^n$ homotopy equivalent to $S^n$

Relationship between Stokes's theorem and the Gauss-Bonnet theorem

A counterexample in topology

Geometric interpretation of the map $SO(4) \to SO(3)$

What, exactly, is the fundamental group of a free loop space?

Mapping class group vs outer automorphism group of the fundamental group for nonorientable surfaces

Can two different topological spaces cover each other?

Fiber bundle with null-homotopic fiber inclusion