New posts in algebraic-topology

Thom–Gysin long exact sequence

reference-request algebraic-topology homology-cohomology exact-sequence sheaf-cohomology

Universal property of the homotopy limit/colimit.

algebraic-topology category-theory homotopy-theory limits-colimits

Euler characteristic: dependence on coefficients

algebraic-topology homology-cohomology betti-numbers

A comparison between the fundamental groupoid and the fundamental group

general-topology algebraic-topology examples-counterexamples groupoids

Euler characteristic, genus and cohomology: a deep connection?

algebraic-geometry differential-geometry algebraic-topology homology-cohomology big-picture

Proof that two spaces that are homotopic have the same de Rham cohomology

algebraic-topology differential-topology

Why are knot invariants best organized as polynomials?

algebraic-topology lie-algebras knot-theory

Homotopy equivalence of a space with the sphere

algebraic-topology homotopy-theory

Why does an orientable surface of genus >1 always have an irregular 3-fold cover?

algebraic-topology

"Proper" definition of a proper map?

general-topology algebraic-geometry algebraic-topology topos-theory

Characteristic map of a n-cell in a CW complex

general-topology algebraic-topology cw-complexes

Homological algebra using nonabelian groups

algebraic-topology homology-cohomology homological-algebra abelian-categories

Proof that retract of contractible space is contractible

general-topology algebraic-topology homotopy-theory

Is the classifying space a fully faithful functor?

algebraic-topology classifying-spaces

Applications or uses of the Serre-Swan theorem

algebraic-topology commutative-algebra noncommutative-geometry

Cross product of cohomology classes: intuition

algebraic-topology soft-question

Universal cover of Möbius band glued to a torus $S^1\times S^1$

general-topology algebraic-topology covering-spaces

Local homeomorphisms which are not covering map?

general-topology algebraic-topology examples-counterexamples covering-spaces

Conjugacy classes in the fundamental group

algebraic-topology fundamental-groups

What categorical limits and colimits does $\pi_1$ preserve?

algebraic-topology category-theory fundamental-groups