30 апр. 2023 г. · A homotopy fiber sequence is a “long left-exact sequence” in an (∞,1)-category. (The dual concept is that of cofiber sequence.) Idea · Definition · Long fibration sequences · Examples

It acts as a homotopy theoretic kernel of a mapping of topological spaces due to the fact it yields a long exact sequence of homotopy groups. Construction · Properties · Examples · Applications

21 февр. 2014 г. · Good definition: X→Y→Z is a homotopy fibration sequence if the composed map is a constant z and the resulting map from X to the homotopy ... Homotopy fibre of composition - at.algebraic topology pullback and fiber sequence - at.algebraic topology Homotopy fiber of a map between classifying spaces Другие результаты с сайта mathoverflow.net

By considering the homotopy fiber Hf instead of the actual fiber, we see that we can obtain a long exact sequence for an arbitrary map f of pointed spaces.

6 мар. 2013 г. · Fiber sequences induce long exact sequences in homotopy, whereas cofiber sequences induce long exact sequences in (co)homology. Therefore the ...

Fibrations and homotopy fiber sequences are powerful tools in algebraic topology. They provide a way to study the global structure of spaces by ...

3 авг. 2016 г. · DEF: X→Y→Z is a homotopy fibration sequence if the composed map is a constant and the resulting map from X to the homotopy fiber of Y→Z is a ...

If 1 → K → G → H → 1 is a short exact sequence of topological groups, applying the classifying space functor gives a fiber sequence B K → B G → B H . Here ...

7 сент. 2022 г. · This gives a common conceptual reason for the following two phenomena: first, the higher étale homotopy groups of X and the geometric fiber X_{ ...

25 мая 2019 г. · The fiber Ff is the homotopy fiber, and consists of pairs (a,γ) with γ a path from f(a) to a basepoint b∈B. At the same time, there are many god ...