The second Johnson homomorphism and the second rational cohomology of the Johnson kernel
Geometric Topology
2019-05-01 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0601314,
title = {The second Johnson homomorphism and the second rational cohomology of the Johnson kernel},
author = {Takuya Sakasai},
journal= {arXiv preprint arXiv:math/0601314},
year = {2019}
}
Comments
24 pages. An insufficient point in the original argument given in Section 4.2 is corrected by the referee's comment. To appear in Math. Proc. Cambridge Philos. Soc