Abelian Extensions of the Group of Diffeomorphisms of a Torus

Yuly Billig

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Abelian Extensions of the Group of Diffeomorphisms of a Torus

Yuly Billig

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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.

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BibTeX RIS

Yuly Billig. 2003-02-01. Abelian Extensions of the Group of Diffeomorphisms of a Torus. https://arxiv.org/abs/math/0302007

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