New posts in algebraic-topology

Are homotopy equivalent path-connected spaces homotopy equivalent as pointed spaces?

general-topology algebraic-topology

Non-normal covering of a Klein bottle by torus.

algebraic-topology

Is every open, bounded and simply connected subset of $\mathbb{R}^n$ essentially a ball?

general-topology algebraic-topology examples-counterexamples

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

algebraic-topology homology-cohomology simplicial-complex

When is $\pi_0$ a group?

algebraic-topology

Some possible mistakes in Bott and Tu [closed]

differential-geometry algebraic-topology

Definition of covering (deck) transformation for smooth manifolds: Are they diffeomorphisms?

differential-geometry algebraic-topology riemannian-geometry covering-spaces

Understanding the trivialisation of a normal bundle

algebraic-topology vector-bundles fiber-bundles

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

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

Homology of complement of a $m$-sphere in $\mathbb R^n$, with $m<n$

algebraic-topology homological-algebra mayer-vietoris-sequence

Proof: A loop is null homotopic iff it can be extended to a function of the disk

algebraic-topology

What is the point of a lift in topology?

general-topology algebraic-topology homotopy-theory

Relations of Characteristic classes: Chern, Stiefel-Whitney, Pontryagin, Euler, Wu class. [closed]

characteristic-classes algebraic-geometry differential-geometry algebraic-topology fiber-bundles

Constant maps induce zero homomorphism

algebraic-topology

Homology of mapping telescope

algebraic-topology homological-algebra homotopy-theory

Is there an orientable closed compact $3$-manifold such that its fundamntal group is $\mathbb{Z}$?

algebraic-topology

Lie groups as manifolds

group-theory differential-geometry algebraic-topology

Intuitive or visual understanding of the real projective plane

algebraic-topology intuition visualization projective-space

Examples of global properties that don't arise from local knowledge

differential-geometry algebraic-topology differential-topology riemannian-geometry

Homology and cohomology of 7-manifold

differential-geometry algebraic-topology manifolds homology-cohomology orientation