New posts in Homology Cohomology

Homology and cohomology of 7-manifold

Is Floer homology always isomorphic to the singular homology of some space?

Intuitive reason why the Euler characteristic is an alternating sum?

Why are we interested in cohomology?

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

counterexample for $f_*:C_*\to D_*$ be a chain map such that $f_*$ induces an isomorphism in homology. Then $f_*$ is a chain homotopy equivalence

Why Cohomology Groups?

On the surjectivity of the Hurewicz homomorphism

Is the pairing induced by the wedge product and integration nondegenerate on de Rham forms?

Is co-cohomology the same as homology?