A fibrationMathworldPlanetmath is a map satisfying the homotopy lifting property. This is easily seen to be equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath to the following:

A map f:XY is a fibration if and only if there is a continuous functionMathworldPlanetmathPlanetmath which given a path, ϕ, in Y and a point, x, lying above ϕ(0), returns a lift of ϕ, starting at x.

Let D2 denote the set of complex numbers with modulus less than or equal to 1. An example of a fibration is the map g:D2[-1,1] sending a complex number z to re(z).

Note that if we restrict g to the boundary of D2, we do not get a fibration. Although we may still lift any path to begin at a prescribed point, we cannot make this assignment continuously.

Another class of fibrations are found in fibre bundles.

Title fibration
Canonical name Fibration
Date of creation 2013-03-22 15:37:57
Last modified on 2013-03-22 15:37:57
Owner whm22 (2009)
Last modified by whm22 (2009)
Numerical id 5
Author whm22 (2009)
Entry type Definition
Classification msc 55R65
Related topic fibremap
Related topic FibreBundle
Related topic LocallyTrivialBundle
Related topic LongExactSequenceLocallyTrivialBundle
Related topic homotopyliftingproperty
Related topic cofibration
Defines fibration