fibration
A fibration is a map satisfying the homotopy lifting property. This is easily seen to be equivalent to the following:
A map is a fibration if and only if there is a continuous function which given a path, , in and a point, , lying above , returns a lift of , starting at .
Let denote the set of complex numbers with modulus less than or equal to 1. An example of a fibration is the map sending a complex number to .
Note that if we restrict to the boundary of , 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 |