On the 2-loop part of the Johnson cokernel

Published 26 Aug 2025 in math.GT, math.AT, and math.QA | (2508.19041v1)

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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