Fiber-Homotopy Equivalence

(Algebraic Topology)


Algebraic Topology
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What is 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 we require a homotopy be a map over B for each time 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 is a homotopy equivalence. If p, q are fibrations, this is always the case for homotopy equivalences by the next proposition. Proposition — Let be fibrations. Then a map over B is a homotopy equivalence if and only if it is a fiber-homotopy equivalence.

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algebraic topologyhomotopy theory

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 — Date merged: 11/6/2021, 1:32:52 PM
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