346 citations · 1.2k across the 23 of their papers we have counts for
10 papers · 1 filter
Generating the Johnson filtration II: finite generation
Thomas Church, Andrew Putman
We prove that every term of the lower central series and Johnson filtrations of the Torelli subgroups of the mapping class group and the automorphism group of a free group are fini…
Generating the Johnson filtration
Thomas Church, Andrew Putman
For k >= 1, let Torelli_g^1(k) be the k-th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k, ther…
Representation stability in cohomology and asymptotics for families of varieties over finite fields
Thomas Church, Jordan S. Ellenberg, Benson Farb
We consider two families X_n of varieties on which the symmetric group S_n acts: the configuration space of n points in C and the space of n linearly independent lines in C^n. Give…
A stability conjecture for the unstable cohomology of SL_n Z, mapping class groups, and Aut(F_n)
Thomas Church, Benson Farb, Andrew Putman
In this paper we conjecture the stability and vanishing of a large piece of the unstable rational cohomology of SL_n Z, of mapping class groups, and of Aut(F_n).
Orbits of curves under the Johnson kernel
Thomas Church
This paper has two main goals. First, we give a complete, explicit, and computable solution to the problem of when two simple closed curves on a surface are equivalent under the Jo…
The rational cohomology of the mapping class group vanishes in its virtual cohomological dimension
Thomas Church, Benson Farb, Andrew Putman
Let Mod_g be the mapping class group of a genus g >= 2 surface. The group Mod_g has virtual cohomological dimension 4g-5. In this note we use a theorem of Broaddus and the combinat…
On the geometric nature of characteristic classes of surface bundles
Thomas Church, Benson Farb, Matthew Thibault
Each Morita--Mumford--Miller (MMM) class e_n assigns to each genus g >= 2 surface bundle S_g -> E^{2n+2} -> M^{2n} an integer e_n^#(E -> M) := <e_n,[M]> in Z. We prove that when n…
Parametrized Abel-Jacobi maps and abelian cycles in the Torelli group
Thomas Church, Benson Farb
Let I_g,* denote the (pointed) Torelli group. This is the group of homotopy classes of homeomorphisms of the genus g >= 2 surface S_g with a marked point, acting trivially on H :=…
Some groups of mapping classes not realized by diffeomorphisms
Mladen Bestvina, Thomas Church, Juan Souto
Let S be a closed surface of genus g >= 2 and z in S a marked point. We prove that the subgroup of the mapping class group Map(S,z) corresponding to the fundamental group pi_1(S,z)…
Separating twists and the Magnus representation of the Torelli group
Thomas Church, Aaron Pixton
The Magnus representation of the Torelli subgroup of the mapping class group of a surface is a homomorphism r: I_{g,1} -> GL_{2g}(Z[H]). Here H is the first homology group of the s…