Explain "homotopy" to me - Mathematics Stack Exchange
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, …
What is the difference between homotopy and homeomorphism?
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, …
Isotopy and Homotopy - Mathematics Stack Exchange
Feb 6, 2013 · What is the difference between homotopy and isotopy at the intuitive level.Some diagrammatic explanation will be helpful for me.
What is the relation between homotopy groups and homology?
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 …
complex analysis - Cauchy's theorem : Homotopy vs Homology ...
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 …
general topology - Homotopy equivalence between spaces …
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 …
Homotopy groups O(N) and SO(N): $\\pi_m(O(N))$ v.s.
Oct 3, 2017 · algebraic-topology lie-groups homotopy-theory higher-homotopy-groups See similar questions with these tags.
algebraic topology - Homotopic, Same homotopy type, homotopy …
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 …
Approximation and homotopy - Mathematics Stack Exchange
Nov 18, 2024 · algebraic-topology differential-topology homotopy-theory transversality See similar questions with these tags.
What is a homotopy pushout? Non-categorical terms please
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 …