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 …

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, …

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 …

Mar 6, 2023 · Yes, precisely. Every homotopy is one of the weaker ones, in the same way that every abelian group is also a group. That doesn't render the definition of "group" meaningless.

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 …

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 …

Mar 11, 2019 · I am currently self-studying the basics of algebraic topology and i just learned the definitions of retract, deformationretract and homotopy equivalence. Now in my book there is …

Dec 14, 2014 · The book Homotopy type theory was written with the intent of assuming as few prerequisites as possible, not even basic algebraic topology or type theory, although it does …

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 …