From loop groups to 2-groups
- J. Baez, Alissa S. Crans, D. Stevenson, U. Schreiber
- Mathematics
- 7 April 2005
We describe an interesting relation between Lie 2-algebras, the Kac– Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where…
Higher Gauge Theory: 2-Connections on 2-Bundles
- J. Baez, U. Schreiber
- Mathematics
- 30 December 2004
Connections and curvings on gerbes are beginning to play a vital role in differential geometry and mathematical physics -- first abelian gerbes, and more recently nonabelian gerbes. These concepts…
Higher gauge theory
- J. Baez, U. Schreiber
- Mathematics
- 29 November 2005
Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings)…
Connections on non-abelian Gerbes and their Holonomy
- U. Schreiber, K. Waldorf
- Mathematics
- 14 August 2008
We introduce an axiomatic framework for the parallel transport of connections on gerbes. It incorporates parallel transport along curves and along surfaces, and is formulated in terms of gluing…
Differential cohomology in a cohesive infinity-topos
- U. Schreiber
- Mathematics
- 29 October 2013
We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we…
Parallel Transport and Functors
- U. Schreiber, K. Waldorf
- Mathematics
- 3 May 2007
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize…
L ∞ -Algebra Connections and Applications to String- and Chern-Simons n-Transport
- H. Sati, U. Schreiber, J. Stasheff
- Mathematics
- 23 January 2008
We give a generalization of the notion of a Cartan-Ehresmann connection from Lie algebras to L ∞-algebras and use it to study the obstruction theory of lifts through higher String-like extensions of…
Cech cocycles for differential characteristic classes -- An infinity-Lie theoretic construction
- D. Fiorenza, U. Schreiber, J. Stasheff
- Mathematics
- 22 November 2010
What are called secondary characteristic classes in Chern-Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider…
Principal ∞-bundles - General theory
- T. Nikolaus, U. Schreiber, D. Stevenson
- Mathematics
- 2012
The theory of principal bundles makes sense in any ∞-topos, such as the ∞-topos of topological, of smooth, or of otherwise geometric ∞-groupoids/∞-stacks, and more generally in slices of these. It…
Differential twisted String and Fivebrane structures
- H. Sati, U. Schreiber, J. Stasheff
- Physics
- 21 October 2009
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