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G-fibration

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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: PB together with a continuous right monoid action P × GP such that

  • (1) for all x in P and g in G.
  • (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.

References

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  1. ^ James, I.M. (1995). Handbook of Algebraic Topology. Elsevier. p. 833. ISBN 978-0-08-053298-1.