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

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 …

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 …

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 …

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 …

Aug 5, 2024 · To sum up, a homotopy pushout is a way to take a span and replace its ordinary pushout by something that behaves like a "homotopy-invariant pushout:" It is defined up to homotopy …

Sep 9, 2013 · The strong definition provides you with an homotopy between 1X 1 X and i ∘ r i ∘ r (one that keeps points of A A fixed during deformation) and the trivial homotopy between 1A 1 A and r ∘ i r …

May 25, 2025 · 0 I just learned that the fact that both adjunction spaces are homotopy equivalent to each other can be seen as an immediate consequence of a general property:

Oct 5, 2017 · Two loops are freely homotopic if there exists a homotopy between. A base point preserving homotopy is one where the homotopy between f and g also satisfies F(x0, t) = x0