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 · Anyways, homotopy equivalence is weaker than homeomorphic. Counterexample to your claim: the 2-dimensional cylinder and a Möbius strip are both 2-dimensional manifolds …
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 …
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.
Non-homotopic spaces with the same homology groups
May 16, 2020 · As for spaces with the same $\pi_*$ but not homeomorphic , this is easy : just take any non-singleton contractible space (such as $\mathbb R$) and more generally homotopy …
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 …
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 …
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 …