On crossed homomorphisms of the volume preserving diffeomorphism groups

Ryoji Kasagawa

Vol. 265 (2013), No. 2, 455–490

DOI: 10.2140/pjm.2013.265.455

Abstract

We construct crossed homomorphisms of the groups of volume preserving diffeomorphisms of closed manifolds with nontrivial first cohomology groups and give their applications to the volume flux groups. Moreover, we see that they descend to crossed homomorphisms of their isotopy groups. In the two dimensional case, we show that their restrictions to Torelli groups are the first Johnson homomorphisms.

Keywords

crossed homomorphisms, volume preserving diffeomorphisms, volume flux groups

Mathematical Subject Classification 2010

Primary: 57R50, 58D05

Secondary: 22E65, 57R15

Milestones

Received: 7 June 2012

Revised: 22 January 2013

Accepted: 4 February 2013

Published: 28 August 2013