New posts in homology-cohomology

What does this map $\mathbb{R}P^\infty\to\mathbb{C}P^\infty$ induce on cohomology?

algebraic-topology homology-cohomology projective-space

$f_*$ induces an isomorphism in homology iff the mapping cone of $f_*$ is contractible.

homological-algebra homology-cohomology

Natural equivalence between singular and simplicial homology

algebraic-topology homology-cohomology simplicial-complex

What is the true relationship between impossible figures and cohomology?

soft-question recreational-mathematics homology-cohomology

Square differential forms in cohomology

differential-geometry homology-cohomology differential-forms de-rham-cohomology

Universal coefficient theorem with ring coefficients

algebraic-topology homological-algebra homology-cohomology

Calculate the cohomology group of $U(n)$ by spectral sequence.

algebraic-topology homology-cohomology sheaf-cohomology spectral-sequences

Homology of a simplicial set

algebraic-topology homology-cohomology simplicial-stuff

Proof of $H^k(X,\mathbf k) = H^k(X,\mathbb Z) \otimes \mathbf k$

manifolds homology-cohomology

Are maps inducing the same cohomology homomorphisms homotopic?

algebraic-topology homotopy-theory homology-cohomology

Cohomology of Grassmannian

algebraic-topology homology-cohomology

Homology and Fundamental group of $\mathbb{R}^4\setminus S^1$

algebraic-topology homology-cohomology fundamental-groups

Finding a space with given homology groups and fundamental group

algebraic-topology homology-cohomology fundamental-groups

Cohomology of complex projective plane

algebraic-topology differential-topology homology-cohomology

$G$-equivariant quasi-ismorphisms over a field

algebraic-topology homology-cohomology homological-algebra equivariant-cohomology

Tensors as matrices vs. Tensors as multi-linear maps

abstract-algebra soft-question differential-geometry homology-cohomology tensors

Can $H_1(\partial \lvert \mathcal R \rvert ) \to H_1(\lvert \mathcal R \rvert)$ be non injective?

algebraic-topology homology-cohomology simplicial-complex

Homology group of $X=\operatorname{SL}(2,\mathbb{R})/\operatorname{SL}(2,\mathbb{Z})$

abstract-algebra group-theory algebraic-topology manifolds homology-cohomology

Homology and cohomology of 7-manifold

differential-geometry algebraic-topology manifolds homology-cohomology orientation

$\pi_1$ and $H_1$ of Symmetric Product of surfaces

algebraic-topology homology-cohomology fundamental-groups