Oct 13, 2020 · But there are some specific homotopy groups, if only outside the stable range, which are not computable by those homological methods. Thus the relation between homotopy groups and …

Feb 10, 2016 · I have been struggling with general topology and now, algebraic topology is simply murder. Some people seem to get on alright, but I am not one of them unfortunately. Please, the …

Jan 18, 2013 · Anyways, homotopy equivalence is weaker than homeomorphic. Counterexample to your claim: the 2-dimensional cylinder and a Möbius strip are both 2-dimensional manifolds and homotopy …

Jan 16, 2026 · In the context of CW-pairs, however, this assumption is for free cause any homotopy equivalence of CW-pairs is a homotopy equivalence of pointed CW-pairs after fixing an arbitrary …

Sep 15, 2019 · Ok, so homotopy equivalence is enough, but why is it better than homeomorphism? The answer is because it makes computations easier. It is much easier to show that two spaces are …

Mar 6, 2023 · Yes, precisely. Every homotopy is one of the weaker ones, in the same way that every abelian group is also a group. That doesn't render the definition of "group" meaningless.

Jun 4, 2025 · homotopy invariance of a functor Ask Question Asked 9 months ago Modified 8 months ago

Nov 18, 2024 · Explore related questions algebraic-topology differential-topology homotopy-theory transversality See similar questions with these tags.

Jul 16, 2025 · The naive homotopy category of pointed spaces has the same objects, and morphisms are homotopy classes of pointed maps (meaning that the base point remains fixed throughout the …

Feb 1, 2025 · However the contours can also be modified by homotopy and cancellation: from which it is also clear that the two integrals are equal. So, what is the advantage of the homology version of …