Fiber-homotopy equivalence

In algebraic topology, a fiber-homotopy equivalence is a map over a space B that has homotopy inverse over B (that is if h t {\displaystyle h_{t}} is a homotopy between the two maps, h t {\displaystyle h_{t}} is a map over B for t.) It is a relative analog of a homotopy equivalence between spaces. Given maps p: D → B, q: E → B, if ƒ: D → E is a fiber-homotopy equivalence, then for any b in B the restriction f : p − 1 ( b ) → q − 1 ( b ) {\displaystyle f:p^{-1}(b)\to q^{-1}(b)} is a homotopy equivalence.

Source: Wikipedia — Fiber-homotopy equivalence (CC BY-SA 4.0)

Fiber-homotopy equivalence

In algebraic topology, a fiber-homotopy equivalence is a map over a space B that has homotopy inverse over B (that is if h t {\displaystyle h_{t}} is a homotopy between the two maps, h t {\displaystyle h_{t}} is a map over B for t.) It is a relative analog of a homotopy equivalence between spaces. Given maps p: D → B, q: E → B, if ƒ: D → E is a fiber-homotopy equivalence, then for any b in B the restriction f : p − 1 ( b ) → q − 1 ( b ) {\displaystyle f:p^{-1}(b)\to q^{-1}(b)} is a homotopy equivalence.

This neuron ends here.

Source: Wikipedia "Fiber-homotopy equivalence" · CC BY-SA 4.0

Share this article: X · Bluesky
Privacy Policy