| Universal Bundle |
Article Index for Universal |
Website Links For Universal |
Information AboutUniversal Bundle |
| CATEGORIES ABOUT UNIVERSAL BUNDLE | |
| homotopy theory | |
M This definition usually takes place within a Category such as the homotopy category of CW Complex es. There, existence theorems for universal bundles arise from Brown's Representability Theorem . The total space of a universal bundle is usually written ''EG''. These spaces are of interest in their own right, despite typically being Contractible . For example in defining the homotopy quotient or '''homotopy orbit space''' of a Group Action of ''G'', in cases where the Orbit Space is Pathological (in the sense of being a non- Hausdorff Space , for example). The idea, if ''G'' acts on the space ''X'', is to consider instead the action on Y and corresponding quotient. See Equivariant Cohomology for more detailed discussion. If ''EG'' is contractible then ''X'' and ''Y'' are Homotopy Equivalent spaces. But the diagonal action on ''Y'', i.e. where ''G'' acts on both ''X'' and ''EG'' coordinates, may be Well-behaved when the action on ''X'' is not. EXAMPLES SEE ALSO EXTERNAL LINK |
|
|