Serre fibration

A Serre fibration is a map having the homotopy lifting property with respect to every disc, equivalently every CW complex.

Table of contents
- Homotopy lifting property Serre fibration
- Long exact sequence of homotopy groups of a fibration Serre fibration

Homotopy lifting property

p : E \to B

has the homotopy lifting property with respect to

X

when every homotopy

X \times I \to B

whose initial map lifts to

E

has a lift extending that initial lift.

Long exact sequence of homotopy groups of a fibration

For a based fibration

F \to E \to B

, lifting representatives defines connecting maps and an exact sequence

\dots \to π_{k} (F) \to π_{k} (E) \to π_{k} (B) \partial π_{k - 1} (F) \to \dots .

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Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 127 / 2 / Solution

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