Higher gauge theory I: 2-Bundles

By T. Bartels. 2004

108 citations recorded by the source corpus.

I categorify the definition of fibre bundle, replacing smooth manifolds with differentiable categories, Lie groups with coherent Lie 2-groups, and bundles with a suitable notion of 2-bundle. To link this with previous work, I show that certain 2-categories of principal 2-bundles are equivalent to certain 2-categories of (nonabelian) gerbes. This relationship can be (and has been) extended to connections on 2-bundles and gerbes. The main theorem, from a perspective internal to this paper, is that the 2-category of 2-bundles over a given 2-space under a given 2-group is (up to equivalence) independent of the fibre and can be expressed in terms of cohomological data (called 2-transitions). From the perspective of linking to previous work on gerbes, the main theorem is that when the 2-space is the 2-space corresponding to a given space and the 2-group is the automorphism 2-group of a given group, then this 2-category is equivalent to the 2-category of gerbes over that space under that group (being described by the same cohomological data).

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Pathology and Forensic Medicine

View Paper: https://www.semanticscholar.org/paper/f1f608c7b7b15256c4a74c440a7a15add527bc8a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Christopher J. Schommer-Pries
2. E. Sharpe
3. John Huerta
4. John C. Baez
5. Urs Schreiber
6. Danny Stevenson
7. Alexander E. Hoffnung
8. A. Henriques

In Nuclear and High Energy Physics

1. E. Sharpe
2. John Huerta
3. John C. Baez
4. Danny Stevenson
5. Urs Schreiber
6. Christopher J. Schommer-Pries
7. Alexander E. Hoffnung
8. Andreas Gustavsson

In Pathology and Forensic Medicine

1. Danny Stevenson
2. Christopher J. Schommer-Pries
3. John C. Baez
4. Alexander E. Hoffnung
5. E. Sharpe
6. Urs Schreiber
7. John Huerta

Citations in the corpus

• The Classifying Space of a Topological 2-Group (2008, background): “However, it turns out [ 6 ] that without loss of generality we may assume that g preserves identity 1-morphisms strictly.”
• Higher gauge theory (2005, background): “The transition functions are maps gij :Uij → Ob(AUT (F )).”
• Convenient Categories of Smooth Spaces (2008, background): “This work had its origin in collaborations between the rst author, Urs Schreiber [3, 4] and Toby Bartels [ 5 ].”
• Notes on generalized global symmetries in QFT (2015, background): “See also [133] for a discussion of bundles of 2-groups, [38, 39] for a discussion of more general bundles of higher groups, and [7][section 3] for a discussion of the relationship between 2-groups and 1-gerbes.”
• An invitation to higher gauge theory (2010, background): “functors between smooth groupoids, and then smooth functors hol : P1(M) → G are in one-to-one correspondence with connections on the trivial principal G-bundle over M. We can go even further: there are more general maps between smooth groupoids, and maps hol : P1(M) → G of this more general sort cor”
• Central extensions of smooth 2–groups and a finite-dimensional string 2–group (2009, background): “ to the bicategoryof smooth stacks and also to the (derived) localization of LieGpdwith respect to the local equivalences [Pro96, Ler08]. This later has a description in terms of ‘smooth anafunctors’ [Bar04]. The Structure and Results of this Paper. The bicategory Bibun, sadly, does not appear to be”