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arXiv · 1201.5052

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

Konrad Waldorf
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Abstract

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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Konrad Waldorf. 2012-05-04. A Construction of String 2-Group Models using a Transgression-Regression Technique. https://doi.org/10.1090/conm%2F584%2F11588

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