Topological complexity of basis-conjugating automorphism groups

关于自由群的基共轭自同构群的Johnson余核的结构

On the structures of the Johnson cokernels of the basis-conjugating automorphism groups of free groups

本文研究自由群的基共轭自同构群的Johnson同构的结构，通过构造障碍条件确定其余核直至四阶，并进一步探讨更高阶的性质。应用中解决了四阶Andreadakis问题，证明了第一上同调群的杯积映射是满射，并计算了自由群的辫子-置换自同构群的扭曲第一上同调群。

Basis-conjugating automorphisms of a free group and associated Lie algebras

Let F_n = <x_1,...,x_n> denote the free group with generators {x_1,...,x_n}. Nielsen and Magnus described generators for the kernel of the canonical epimorphism from the automorphism group of F_n to the general linear group over the integers. In particular among them are the automorphisms chi_{k,i} which conjugate the generator x_k by the generator x_i leaving the x_j fixed for j not k. A computation of the cohomology ring as well as the Lie algebra obtained from the descending central series of the group generated by chi_{k,i} for i<k is given here. Partial results are obtained for the group …

The structure of the group of conjugating automorphisms and the linear representation of the braid groups of some manifolds

In this paper we describe the structure of a group of conjugating automorphisms $C_n$ of free group and prove that this structure is similar to the structure of a braid group $B_n$ with $n>1$ strings. We find the linear representation of group $C_n$. Also we prove that the braid group $B_n(S^2)$ of 2--sphere, mapping class group M(0,n) of the $n$--punctured 2--sphere and the braid group $B_3(P^2)$ of the projective plane are linear. Using result of J. Dyer, E. Formanek, E. Grossman and the faithful linear representation of Lawrence--Krammer of $B_4$ we construct faithful linear representation …

同伦下辫子与焊接辫子的Milnor不变量

Milnor invariants of braids and welded braids up to homotopy

本文研究同伦下纯焊接辫子群的结构，通过将其商群分解为迭代半直积解决Andreadakis问题并给出生成元表示，同时关联Milnor不变量并讨论经典辫子的对应情况。