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 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 …
What is the difference between homotopy and homeomorphism?
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 …
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.
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.
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 …
About Homotopy lifting property - Mathematics Stack Exchange
Sep 14, 2020 · The homotopy lifting property shows that any path homotopy $h_t : f \simeq g$ lifts to a homotopy $\tilde h_t$ starting with $\tilde f$. But it is not a priori clear that that $\tilde h_t$ …
Approximation and homotopy - Mathematics Stack Exchange
Nov 18, 2024 · Explore related questions algebraic-topology differential-topology homotopy-theory transversality See similar questions with these tags.
Homotopy equivalence of pairs - Mathematics Stack Exchange
May 23, 2018 · Homotopy equivalence of pairs Ask Question Asked 7 years, 7 months ago Modified 1 year, 6 months ago
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 …