AI 中文总结
针对亏格g≥3且至多一个边界分支的曲面，研究给出Birman-Craggs-Johnson同态的核与Torelli群换位子群的显式生成元集，还给出Johnson关于Torelli群阿贝尔化计算的新证明。
AI 中文摘要
对于亏格g≥3且至多有一个边界分支的曲面，我们给出Birman-Craggs-Johnson同态的核以及Torelli群的换位子群的显式生成元集；作为应用，我们给出Johnson关于Torelli群阿贝尔化计算的新证明。
英文摘要
For surfaces of genus $g \geq 3$ with at most one boundary component, we give explicit generating sets for the kernel of the Birman-Craggs-Johnson homomorphism and the commutator subgroup of the Torelli group. As an application, we give a new proof of Johnson's calculation of the abelianization of the Torelli group.
Comments33 pages, 13 figures
