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 …

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.

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 …

May 23, 2018 · Homotopy equivalence of pairs Ask Question Asked 7 years, 6 months ago Modified 1 year, 6 months ago

May 9, 2015 · Your argument for homotopy implying contractability is formally correct, but I am unsure how one would avoid circularity - from where do you get the fact that $ [Cf, Z]=0$? The …

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 …

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 $\tilde h_t$ …

Oct 5, 2017 · Base Point Homotopy vs Free Homotopy Example Ask Question Asked 8 years, 2 months ago Modified 8 years, 2 months ago