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 = idB.
> 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];
Bunk a2102
[in geometry, field theory, and quantisation, rev].
@ Geometry:
Stevenson PhD(00)m.DG.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 24 feb 2021