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 · 67 What is the difference between homotopy and homeomorphism? Let X and Y be two spaces, Supposed X and Y are homotopy equivalent and have the same dimension, can it be proved …

Feb 6, 2013 · What is the difference between homotopy and isotopy at the intuitive level.Some diagrammatic explanation will be helpful for me.

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 …

Dec 13, 2025 · I am studying homotopy theory and this question occurred to me: Why we can't use coverings to calculate higher homotopy groups? I know that are other techniques to compute higher …

Oct 3, 2017 · The first uses the action of SO(n) S O (n) on Sn−1 ⊆Rn S n − 1 ⊆ R n, the second is the determinant and the third is the universal cover. Hence all of O(n) O (n), SO(n) S O (n), Spin(n) S p i …

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 …

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 …

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 …

Dec 1, 2017 · In my opinion, the adjective "homotopic" should only apply to maps, and for spaces we should reserve the term "homotopy equivalent". "Same homotopy type" and "homotopy equivalent' …