Magnus和Burau表示的核的无限生成
Infinite generation of the kernels of the Magnus and Burau representations
摘要：
考虑Torelli群的Magnus表示的核Mag_g和辫群的Burau表示的核Bur_n。证明了当g >= 2，n >= 6时，群Mag和Bur n有无穷秩一阶同调.因此，我们得出结论，没有任何组有任何有限的生成集。在每种情况下的证明方法包括生产一种“约翰逊型”同态的无限秩阿贝尔群，并证明图像有无限的秩。对于Bur_n的情形，我们借助于计算机计算来完成.
英文摘要：
Consider the kernel Mag_g of the Magnus representation of the Torelli group and the kernel Bur_n of the Burau representation of the braid group. We prove that for g >= 2 and for n >= 6 the groups Mag_g and Bur_n have infinite rank first homology. As a consequence we conclude that neither group has any finite generating set. The method of proof in each case consists of producing a kind of "Johnson-type" homomorphism to an infinite rank abelian group, and proving the image has infinite rank. For the case of Bur_n, we do this with the assistance of a computer calculation.
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