The second Johnson homomorphism and the second rational cohomology of the Johnson kernel

Details The second Johnson homomorphism and the second rational cohomology of the Johnson kernel The second Johnson homomorphism and the second rational cohomology of the Johnson kernel

2006-01-13

arxiv.org/abs/math/0601314v2

Mathematical Proceedings of the Cambridge Philosophical Society 143 (2007), 627-648

Mathematics

Geometric Topology

24 pages. An insufficient point in the original argument given in Section 4.2 is corrected by the referee's comment. To appear

Scientific paper

The Johnson kernel is the subgroup of the mapping class group of a surface generated by Dehn twists along bounding simple closed curves, and has the second Johnson homomorphism as a free abelian quotient. In terms of the representation theory of the symplectic group, we give a complete description of cup products of two classes in the first rational cohomology of the Johnson kernel obtained by the rational dual of the second Johnson homomorphism.

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