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}
}
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32 pages