The first Galois obstruction in the Johnson cokernel

Shigeyuki Morita; Takuya Sakasai; Masaaki Suzuki

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arXiv · 2608.17673

The first Galois obstruction in the Johnson cokernel

Shigeyuki Morita·Takuya Sakasai·Masaaki Suzuki

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Abstract

We explicitly determine the first Galois obstruction in the cokernel of the Johnson homomorphism of the mapping class group of a surface of genus $g$, for every genus $g \ge 2$. It is described as a sum of two terms which are considerably different in character. One lies in the kernel of the Enomoto-Satoh trace map, whereas the other belongs to a certain ideal which vanishes upon passage to the closed surface case.

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Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki. 2026-08-18. The first Galois obstruction in the Johnson cokernel. https://arxiv.org/abs/2608.17673

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