Abelian Extensions of the Group of Diffeomorphisms of a Torus
Group Theory
2007-05-23 v1
Abstract
In this paper we construct abelian extensions of the group of diffeomorphisms of a torus. We consider the jacobian map, which is a crossed homomorphism from the group of diffeomorphisms into a toroidal gauge group. A pull-back under this map of a central 2-cocycle on a gauge group turns out to be an abelian cocycle on the group of diffeomorphisms. We show that in the case of a circle, the Virasoro-Bott cocycle is a pull-back of the Heisenberg cocycle. We also give an abelian generalization of the Virasoro-Bott cocycle to the case of a manifold with a volume form.
Keywords
Cite
@article{arxiv.math/0302007,
title = {Abelian Extensions of the Group of Diffeomorphisms of a Torus},
author = {Yuly Billig},
journal= {arXiv preprint arXiv:math/0302007},
year = {2007}
}
Comments
14 pages