A Construction of String 2-Group Models using a Transgression-Regression Technique

Details A Construction of String 2-Group Models using a Transgression-Regression Technique A Construction of String 2-Group Models using a Transgression-Regression Technique

2012-01-24

arxiv.org/abs/1201.5052v1

Mathematics

Differential Geometry

25 pages

Scientific paper

In this note we present a new construction of the string group that ends optionally in two different contexts: strict diffeological 2-groups or finite-dimensional Lie 2-groups. It is canonical in the sense that no choices are involved; all the data is written down and can be looked up (at least somewhere). The basis of our construction is the basic gerbe of Gawedzki-Reis and Meinrenken. The main new insight is that under a transgression-regression procedure, the basic gerbe picks up a multiplicative structure coming from the Mickelsson product over the loop group. The conclusion of the construction is a relation between multiplicative gerbes and 2-group extensions for which we use recent work of Schommer-Pries.

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