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 …
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 …
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.
Homotopy equivalence vs. Homeomorphism vs. Ambient isotopy
Dec 10, 2020 · Homotopy equivalence vs. Homeomorphism vs. Ambient isotopy Ask Question Asked 4 years, 11 months ago Modified 4 years, 11 months ago
algebraic topology - Base Point Homotopy vs Free Homotopy …
Oct 5, 2017 · Base Point Homotopy vs Free Homotopy Example Ask Question Asked 8 years, 1 month ago Modified 8 years, 1 month ago
Definitions of free and based homotopy. - Mathematics Stack …
Definitions of free and based homotopy. Ask Question Asked 8 years, 8 months ago Modified 8 years, 8 months ago
Notations involving squiggly lines over horizontal lines
Sep 28, 2011 · 3 I agree with Qiaochu Yuan's answer for the most part, but if you are working in an area where you must distinguish between homeomorphism, homotopy equivalence, and …
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 …