John Baez

2007 Abel Symposium

August 8, 2007

Higher Gauge Theory and Elliptic Cohomology

The concept of elliptic object suggests a relation between elliptic cohomology and "higher gauge theory", a generalization of gauge theory describing the parallel transport of strings. In higher gauge theory, we categorify familiar notions from gauge theory and consider "principal 2-bundles" with a given "structure 2-group". These are a slight generalization of nonabelian gerbes. After a quick introduction to these ideas, we focus on the 2-groups Stringk(G) associated to any compact simple Lie group G. We describe how these 2-groups are built using central extensions of the loop group ΩG, and how the classifying space for Stringk(G)-2-bundles is related to the "string group" familiar in elliptic cohomology. If there is time, we shall also describe a vector 2-bundle canonically associated to any principal 2-bundle, and how this relates to the von Neumann algebra construction of Stolz and Teichner.
Click on this to see the transparencies of the talk: This talk is based on joint work with Toby Bartels, Alissa Crans, Danny Stevenson and Urs Schreiber: For elliptic cohomology, see: For closely related work on higher gauge theory, see:

© 2007 John Baez