AI 中文总结
本文证明亏格g≥6时，第三约翰逊同态τ₃的像与带一个边界分支曲面Σ_{g,1}的森田迹映射的核重合，且τ₃在手柄体子群上的像为两类迹映射核的交集。
AI 中文摘要
本文中，当亏格g≥6时，我们证明了对于带一个边界分支的曲面Σ_{g,1}，第三约翰逊同态τ₃的像与森田迹映射的核重合。此外，作为推论，我们得到τ₃在手柄体子群上的像，与森田迹映射和拉格朗日迹映射的核的交集重合。
英文摘要
In this note we show that the image of the third Johnson homomorphism $τ_3$ coincides with the kernel of Morita's trace map for the case of a surface of genus $g$ with one boundary component $Σ_{g,1}$, when $g \geq 6$. Moreover, as a consequence, we get that the image of $τ_3$ on the handlebody subgroups coincides with the intersection of kernels of the Morita trace map and the Lagrangian trace maps.
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