long exact sequence (locally trivial bundle)
Let is a locally trivial bundle, with fiber . Then there is a long exact sequence of homotopy groups
Here is induced by the inclusion as the fiber over the basepoint of , and is the following map: if , then lifts to a map of into (that is a map of the -disk into , taking its boundary to ), sending the basepoint on the boundary to the base point of . Thus the map on , the -sphere, defines an element of . This is . The covering homotopy property of a locally trivial bundle shows that this is well-defined.
|Title||long exact sequence (locally trivial bundle)|
|Date of creation||2013-03-22 13:14:58|
|Last modified on||2013-03-22 13:14:58|
|Last modified by||bwebste (988)|