Lie groups of bisections of a Lie groupoid

29.05.2019, *14:00 Uhr*  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Alexander Schmeding (Technische Universität Berlin)

To a Lie groupoid one can associate an infinite dimensional Lie group, the so called bisection group.
These groups are closely connected to the geometry and representation theory of the underlying Lie groupoid.
To give an example, for the pair groupoid of a manifold, the bisection group recovers the diffeomorphism group of
the manifold. In this talk we will briefly review the infinite dimensional Lie group structure on the bisection group.
Then we will explain how this leads to a Lie group structure on the subgroup of vertical bisections. These subgroups
arise naturally in geometry: If the Lie groupoid is the gauge groupoid of a principal bundle, its bisection group can be
identified with the group of bundle automorphisms, while the vertical bisections correspond then to the gauge group
of the bundle.