A Smooth Model for the String Group

Understand

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.