(2) For each x in P, the map is a weak equivalence.
A principal G-bundle is a prototypical example of a G-fibration. Another example is Moore's path space fibration: namely, let be the space of paths of various length in a based space X. Then the fibration that sends each path to its end-point is a G-fibration with G the space of loops of various lengths in X.
Referencesedit
^James, I.M. (1995). Handbook of Algebraic Topology. Elsevier. p. 833. ISBN978-0-08-053298-1.
This topology-related article is a stub. You can help Wikipedia by expanding it.
fibration, algebraic, topology, principal, fibration, generalization, principal, bundle, just, fibration, generalization, fiber, bundle, definition, given, topological, monoid, fibration, together, with, continuous, right, monoid, action, such, that, displayst. In algebraic topology a G fibration or principal fibration is a generalization of a principal G bundle just as a fibration is a generalization of a fiber bundle By definition 1 given a topological monoid G a G fibration is a fibration p P B together with a continuous right monoid action P G P such that 1 p xg p x displaystyle p xg p x for all x in P and g in G 2 For each x in P the map G p 1 p x g xg displaystyle G to p 1 p x g mapsto xg is a weak equivalence A principal G bundle is a prototypical example of a G fibration Another example is Moore s path space fibration namely let P X displaystyle P X be the space of paths of various length in a based space X Then the fibration p P X X displaystyle p P X to X that sends each path to its end point is a G fibration with G the space of loops of various lengths in X References edit James I M 1995 Handbook of Algebraic Topology Elsevier p 833 ISBN 978 0 08 053298 1 nbsp This topology related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title G fibration amp oldid 918740937, wikipedia, wiki, book, books, library,