Bundles |

**In General**

* __Idea__: A generalization
of fiber bundles, in which the condition of a local product structure is dropped.

$ __Def__: A triple (*E*,* B*,
*π*), with *E*, *B* ∈ Top and *π*:* E* →
*B* continuous and surjective; *B* is called the base space, and
*π* the projection map.

$ __Cross section__:
Given a bundle (*E*,* B*, *π*),
a cross section is a map *f* : *B* → *E*, such that
*π* \(\circ\) *f* = id_{B}.

> __Other special types__:
see Wikipedia page.

**Special Types**

* __Examples__: The most common
ones are fiber bundles (> see fiber bundles).

> __Other special types__:
see Path [bundles over path spaces];
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-fs [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 PhD(00)m.DG.

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send feedback and suggestions to bombelli at olemiss.edu – modified 17 jan 2016