New posts in homology-cohomology

vector bundles on affine schemes

algebraic-geometry homology-cohomology

Is the Euler characteristic of $\mathbb{R}^n$ $1$ or $(-1)^n$?

algebraic-topology homology-cohomology

What is the geometric intuition for the $\bar \partial$-Poincare lemma, or for $\bar \partial$ more generally?

complex-analysis homology-cohomology intuition complex-geometry complex-integration

Does de Rham theorem hold for manifolds with boundary?

differential-topology homology-cohomology smooth-manifolds

cup product in cohomology ring of a suspension

algebraic-topology homology-cohomology homotopy-theory geometric-topology cw-complexes

Chain homotopy inverse to inclusion

algebraic-topology homology-cohomology

Twisted Cech cohomology

reference-request algebraic-topology homology-cohomology

Singular homology with coefficients in a ring versus in an abelian group

algebraic-topology soft-question homology-cohomology homological-algebra abelian-groups

Computing the homology groups of the twice-punctured disk

algebraic-topology homology-cohomology

What are cohomology rings good for?

algebraic-topology homology-cohomology

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

graph-theory algebraic-topology homology-cohomology

Applications for Homology

general-topology algebraic-topology applications homology-cohomology

Why are de Rham cohomology and Cech cohomology of the constant sheaf the same

differential-geometry manifolds sheaf-theory homology-cohomology differential-forms

Why group cohomology and not group homology?

soft-question homology-cohomology homological-algebra group-cohomology

Question about Singular Homology section in Hatcher

algebraic-topology manifolds homology-cohomology

integral cohomology ring of real projective space

algebraic-geometry algebraic-topology homology-cohomology projective-space cw-complexes

The "need" for cohomology theories

soft-question homology-cohomology

Linear action induced in homology of the $n$-dimensional torus

algebraic-topology dynamical-systems homology-cohomology

Torsion in the integral (co)homology of Eilenberg-MacLane spaces

algebraic-topology homology-cohomology eilenberg-maclane-spaces

Show $\mathbb{CP^2/CP^1}$ is not a retract of $\mathbb{CP^4/CP^1}$.

algebraic-topology homology-cohomology