Bundles

In General
$ Def: A triple (E, B, ), with E and B in Top and : E → B continuous and surjective; B is called the base space, and the projection map.
$ Cross section: Given a bundle (E, B, ), a cross section is a map f : B → E, such that f = id_B.

Special Types
* Examples: The most common ones are fiber bundles (> see fiber bundles).
> Other special types: see posets [bundles over posets]; sheaves.

Related Concepts
$ Bundle map: A continuous map f : E → F, where E and F are two bundles, which carries each fiber of E isomorphically onto a fiber of F.
> Other related concepts: see Fibrations.

Bundle Gerbe > s.a. Gerbe.
* Idea: Every bundle gerbe gives rise to a gerbe, and most of the well-known examples of gerbes are bundle gerbes.
@ General references: Murray JLMS(96)dg/94; Murray & Stevenson JLMS(00)m.DG/99; Bouwknegt et al CMP(02)ht/01 [K-theory]; Gawedzki & Reis JGP(04) [over connected compact simple Lie groups]; Murray a0712-in [intro].
@ In field theory: Carey et al RVMP(00)ht/97; Ekstrand & Mickelsson CMP(00)ht/99; Gomi ht/01 [Chern-Simons theory]; Carey et al CMP(05)m.DG/04 [Chern-Simons and Wess-Zumino-Witten theories].
@ Geometry: Stevenson m.DG/00-PhD.

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 18 jun 2008