New posts in homotopy-theory

Higher categories for category theorists?

reference-request category-theory homotopy-theory simplicial-stuff higher-category-theory

Is the punctured plane homotopy equivalent to the circle?

general-topology homotopy-theory

Homotopy equivalence induces bijection between path components

algebraic-topology homotopy-theory connectedness

17 definitions of algebraic K-theory of a ring. Which should I take?

number-theory algebraic-geometry homotopy-theory algebraic-k-theory

Manifold without point homotopy equivalent to wedge of $2$-spheres.

general-topology algebraic-topology manifolds homology-cohomology homotopy-theory

Fat geometric realization weakly equivalent to the usual one

algebraic-topology homotopy-theory simplicial-stuff

Homotopy groups O(N) and SO(N): $\pi_m(O(N))$ v.s. $\pi_m(SO(N))$

algebraic-topology lie-groups homotopy-theory higher-homotopy-groups

Proving directly that $S^2$ is simply connected: is a surjective loop homotopic to a non-surjective one?

algebraic-topology homotopy-theory fundamental-groups

A problem on algebraic topology.

algebraic-topology homology-cohomology homotopy-theory higher-category-theory

Proving homotopy equivalence of a torus with points removed

algebraic-topology homotopy-theory

Every "star-shaped" set is simply connected

complex-analysis homotopy-theory

Two Homotopy Colimit Questions

algebraic-topology homotopy-theory

Are close maps homotopic?

differential-topology homotopy-theory

The circle is not contractible

general-topology algebraic-topology homotopy-theory

homotopic maps from the sphere to the sphere

algebraic-topology homotopy-theory

Maps to Sn homotopic

algebraic-topology homotopy-theory

Homotopy equivalence of two different gluings of $B^n$ and an arbitrary space $X$

algebraic-topology homotopy-theory

Can Spectra be described as abelian group objects in the category of Spaces? (in some appropriate $\infty$-sense)

homotopy-theory higher-category-theory

Are maps inducing the same cohomology homomorphisms homotopic?

algebraic-topology homotopy-theory homology-cohomology

What is the point of a lift in topology?

general-topology algebraic-topology homotopy-theory