David Roberts 2-bundle

Idea

2-bundles are a categorification of the usual notion of bundle. Most often principal 2-bundles are treated, but there is interest in 2-vector bundles for the purposes of interpreting elliptic cohomology.

Papers

The seminal work on 2-bundles is Toby Bartel’s PhD thesis:

  • Higher Gauge Theory I: 2-bundles (webpage)

which covers principal 2-bundles, internal category theory, anafunctors, associated 2-bundles, descent data for 2-bundles. Toby introduced internal anafunctors and my thesis draws heavily on that material (covering it in my own way).

There are other papers that deal with 2-bundles, or related objects, such as Igor Bakovic’s PhD thesis (principal bigroupoid bundles), and various papers referenced at the nLab page on principal 2-bundles.

For stuff on 2-vector bundles see work by Nils Baas and coworkers: Two-vector bundles and forms of elliptic cohomology, Two-Categorical Bundles and Their Classifying Spaces.

(rough) Definition

A 2-bundle on a topological space XX is a topological groupoid EXE \to X over XX such that there is an open cover UXU \to X and an equivalence U× XEU×FU\times_X E \to U \times F in the bicategory Ana/UAna/U of anafunctors over UU, where FF is some topological groupoid.

Last revised on April 10, 2012 at 13:36:13. See the history of this page for a list of all contributions to it.