English

On the 2-loop part of the Johnson cokernel

Geometric Topology 2025-12-01 v2 Algebraic Topology Quantum Algebra

Abstract

We study stable Sp-decompositions of the cokernel of the Johnson homomorphism. Continuing the work of Conant in 2016, which identified the 1-loop part of the Johnson cokernel as the Enomoto-Satoh obstruction, we study the 2-loop part. Using the corresponding 2-loop trace map, we capture all the components of the Johnson cokernels in degree 6 that cannot be detected by the Enomoto-Satoh trace.

Cite

@article{arxiv.2508.19041,
  title  = {On the 2-loop part of the Johnson cokernel},
  author = {Yusuke Kuno and Masatoshi Sato},
  journal= {arXiv preprint arXiv:2508.19041},
  year   = {2025}
}

Comments

32 pages

R2 v1 2026-07-01T05:06:47.764Z