On the 2-loop part of the Johnson cokernel

Yusuke Kuno; Masatoshi Sato

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arXiv · 2508.19041

On the 2-loop part of the Johnson cokernel

Yusuke Kuno·Masatoshi Sato

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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.

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Yusuke Kuno, Masatoshi Sato. 2025-08-26. On the 2-loop part of the Johnson cokernel. https://arxiv.org/abs/2508.19041

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