Friedrich Wagemann

Lie group structures on groups of smooth and holomorphic maps on non-compact manifolds

We study Lie group structures on groups of the form C∞(M, K), where M is a non-compact smooth manifold and K is a, possibly infinite-dimensional, Lie group. First we prove that there is at most one Lie group structure with Lie algebra

The second cohomology of current algebras of general Lie algebras

C^\infty(M, {\mathfrak{k}})

Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles

for which the evaluation map is smooth. We then prove the existence of such a structure if the universal cover of K is diffeomorphic to a locally convex space and if the image of the left logarithmic derivative in

A Crossed Module Representing the Godbillon–Vey Cocycle

\Omega^1(M, {\mathfrak{k}})

A two-dimensional analogue of the Virasoro algebra

is a smooth submanifold, the latter being the case in particular if M is one-dimensional. We also obtain analogs of these results for the group