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Proceedings of the London Mathematical Society Advance Access published online on June 16, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp023
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© 2009 London Mathematical Society

A Maslov cocycle for unitary groups

Linus Kramer and Katrin Tent

Mathematisches Institut
Universität Münster
Einsteinstr. 62
48149 Münster
Germany
tent@uni-muenster.de

Received 24 September 2008.

We introduce a 2-cocycle for symplectic and skew-hermitian hyperbolic groups over arbitrary fields and skew-fields, with values in the Witt group of hermitian forms. This cocycle has good functorial properties: it is natural under extension of scalars and stable, and so it can be viewed as a universal 2-dimensional characteristic class for these groups. Over R and C, it coincides with the first Chern class.

The authors were supported by SFB 478 and SFB 701.

2000 Mathematics Subject Classification 11E70, 19C09, 20G10, 20J05.


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