May 12, 2025

Computations on Johnson cokernels

Sakasai Takuya*, The University of Tokyo, Japan RIMS Kyoto (Room 201, Building No. 15) + Zoom · JP: 15:30 · FR: 08:30

The Johnson homomorphisms serve as fundamental tools for the algebraic study of the mapping class group of a surface. Determining the cokernel has been an important problem and the Enomoto-Satoh obstruction (trace) provides a major part of the cokernel. In this talk, we discuss those Johnson cokernels that cannot be detected by the Enomoto-Satoh obstruction.
If time permits, we will further discuss topological implications of Johnson cokernels such as invariants of homology cobordisms of surfaces and rational cohomology classes of moduli spaces of graphs.
This talk is based on joint works with Shigeyuki Morita and Masaaki Suzuki, and with Gwenael Massuyeau.

* Speaker by Zoom

  1. Shigeyuki Morita, Masaaki Suzuki, Takuya Sakasai, Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras. Advances in Mathematics 282 (2015), 291-334.
  2. Gwenael Massuyeau, Takuya Sakasai, Morita's trace maps on the group of homology cobordisms. Journal of Topology and Analysis, 12 (2020), 775-818.

 To the main page of the AHGT seminar.