A Smooth Model for the String Group

Abstract

We construct a model for the string group as an infinite-dimensional Lie group. In a second step, we extend this model by a contractible Lie group to a Lie 2-group model. To this end, we need to establish some facts on the homotopy theory of Lie 2-groups. Moreover, we provide an explicit comparison of string structures for the two models and a uniqueness result for Lie 2-group models.