a collection of continuous maps called transition functions
the map given by is a homeomorphism for each ,
for all indices and , and
for all indices and , .
Readers familiar with Čech cohomology may recognize condition 3), it is often called the cocycle condition. Note, this imples that is the identity in for each , and .
If the total space is homeomorphic to the product so that the bundle projection is essentially projection onto the first factor, then is called a trivial bundle. Some examples of fiber bundles are vector bundles and covering spaces.
There is a notion of morphism of fiber bundles over the same base with the same structure group . Such a morphism is a -equivariant map , making the following diagram commute
Thus we have a category of fiber bundles over a fixed base with fixed structure group.
|Date of creation||2013-03-22 13:07:06|
|Last modified on||2013-03-22 13:07:06|
|Last modified by||bwebste (988)|