For k 1, let I1g (k) be the kth term in the Johnson ltration of the mapping class group of a genus g surface with one boundary component. We prove that for all k 1, there exists some Gk 0 such that I1g (k) is generated by elements which are supported on subsurfaces whose genus is at most Gk. We also prove similar theorems for the Johnson ltration of Aut(Fn) and for certain mod-p analogues of the Johnson ltrations of both the mapping class group and of Aut(Fn). The main tools used in the proofs are the related theories of FI-modules (due to the rst author with Ellenberg and Farb) and central stability (due to the second author), both of which concern the representation theory of the symmetric groups over Z
Let Σ be a compact connected oriented surface with one boundary component and let M denote the mappi...
Let Modg,b denote the mapping class group of a surface of genus g with b punctures. Luo asked in [T...
A well-known conjecture asserts that the mapping class group of a surface (possibly with punctures/b...
For k≥1, let J1g(k) be the k th term in the Johnson filtration of the mapping class group of a genus...
International audienceThe Johnson filtration of the mapping class group of a compact, oriented surfa...
We prove that every term of the lower central series and Johnson filtrations of the Torelli subgroup...
9 pagesWe show that the first Johnson subgroup of the mapping class group of a surface S of genus gr...
We consider two mod-p central series of the free group given by Stallings and Zassenhaus. Applying t...
ABSTRACT. Let $\Sigma_{g,1} $ be an orientable compact surface of genus $g $ with 1 boundary compone...
We show that the first Johnson subgroup of the mapping class group of a surface Σ of genus greater t...
Let $F_n(\Sigma_{g,1})$ denote the configuration space of $n$ ordered points on the surface $\Sigma_...
62 pagesThe Johnson-Morita theory is an algebraic approach to the mapping class group of a surface $...
This paper has two main goals. First, we give a complete, explicit, and computable solution to the p...
AbstractLet Modg,b denote the mapping class group of a surface of genus g with b punctures. Luo aske...
Let K(S) be the subgroup of the extended mapping class group, Mod(S), generated by Dehn twists about...
Let Σ be a compact connected oriented surface with one boundary component and let M denote the mappi...
Let Modg,b denote the mapping class group of a surface of genus g with b punctures. Luo asked in [T...
A well-known conjecture asserts that the mapping class group of a surface (possibly with punctures/b...
For k≥1, let J1g(k) be the k th term in the Johnson filtration of the mapping class group of a genus...
International audienceThe Johnson filtration of the mapping class group of a compact, oriented surfa...
We prove that every term of the lower central series and Johnson filtrations of the Torelli subgroup...
9 pagesWe show that the first Johnson subgroup of the mapping class group of a surface S of genus gr...
We consider two mod-p central series of the free group given by Stallings and Zassenhaus. Applying t...
ABSTRACT. Let $\Sigma_{g,1} $ be an orientable compact surface of genus $g $ with 1 boundary compone...
We show that the first Johnson subgroup of the mapping class group of a surface Σ of genus greater t...
Let $F_n(\Sigma_{g,1})$ denote the configuration space of $n$ ordered points on the surface $\Sigma_...
62 pagesThe Johnson-Morita theory is an algebraic approach to the mapping class group of a surface $...
This paper has two main goals. First, we give a complete, explicit, and computable solution to the p...
AbstractLet Modg,b denote the mapping class group of a surface of genus g with b punctures. Luo aske...
Let K(S) be the subgroup of the extended mapping class group, Mod(S), generated by Dehn twists about...
Let Σ be a compact connected oriented surface with one boundary component and let M denote the mappi...
Let Modg,b denote the mapping class group of a surface of genus g with b punctures. Luo asked in [T...
A well-known conjecture asserts that the mapping class group of a surface (possibly with punctures/b...