105 citations · 705 across the 54 of their papers we have counts for
36 papers · 1 filter
The rational homology of quotients of the curve complex
Andrew Putman
Let be the mapping class group of a genus- surface with punctures and let be its curve complex. For a finite-index subgroup $G < \ma…
The kernel of the Birman-Craggs-Johnson homomorphism
Tara E. Brendle, Dan Margalit, Andrew Putman
For surfaces of genus with at most one boundary component, we give explicit generating sets for the kernel of the Birman-Craggs-Johnson homomorphism and the commutator s…
Calculating the second rational cohomology group of the Torelli group
Andrew Putman
Minahan and the author recently proved results that allow the calculation of the second rational cohomology group of the Torelli group. This builds on two key ingredients: Hain's c…
Generating the homology of covers of surfaces
Marco Boggi, Andrew Putman, Nick Salter
Putman and Wieland conjectured that if is a finite branched cover between closed oriented surfaces of sufficiently high genus, then the orbits of all nonzer…
The commutator subgroups of free groups and surface groups
Andrew Putman
A beautifully simple free generating set for the commutator subgroup of a free group was constructed by Tomaszewski. We give a new geometric proof of his theorem, and show how to g…
The mapping class group of connect sums of
Tara Brendle, Nathan Broaddus, Andrew Putman
Let be the connect sum of copies of . A classical theorem of Laudenbach says that the mapping class group is an extension of $\text{Out}…
The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary
Tara Brendle, Nathan Broaddus, Andrew Putman
We give two proofs that appropriately defined congruence subgroups of the mapping class group of a surface with punctures/boundary have enormous amounts of rational cohomology in t…
Partial Torelli groups and homological stability
Andrew Putman
We prove a homological stability theorem for the subgroup of the mapping class group acting as the identity on some fixed portion of the first homology group of the surface. We als…
Equivariant group presentations and the second homology group of the Torelli group
Martin Kassabov, Andrew Putman
We develop a theory of equivariant group presentations and relate them to the second homology group of a group. Our main application says that the second homology group of the Tore…
Surface groups, infinite generating sets, and stable commutator length
Dan Margalit, Andrew Putman
We give a new proof of a theorem of D. Calegari that says that the Cayley graph of a surface group with respect to any generating set lying in finitely many mapping class group orb…
Simple closed curves, finite covers of surfaces, and power subgroups of Out(F_n)
Justin Malestein, Andrew Putman
We construct examples of finite covers of punctured surfaces where the first rational homology is not spanned by lifts of simple closed curves. More generally, for any set $\mathca…
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…
The high-dimensional cohomology of the moduli space of curves with level structures
Neil Fullarton, Andrew Putman
We prove that the moduli space of curves with level structures has an enormous amount of rational cohomology in its cohomological dimension. As an application, we prove that the co…
A Birman exact sequence for the Torelli subgroup of Aut(F_n)
Matthew B. Day, Andrew Putman
We develop an analogue of the Birman exact sequence for the Torelli subgroup of Aut(F_n). This builds on earlier work of the authors who studied an analogue of the Birman exact seq…
On the second homology group of the Torelli subgroup of Aut(F_n)
Matthew B. Day, Andrew Putman
Let IA_n be the Torelli subgroup of Aut(F_n). We give an explicit finite set of generators for H_2(IA_n) as a GL_n(Z)-module. Corollaries include a version of surjective representa…
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…
Pseudo-Anosov dilatations and the Johnson filtration
Justin Malestein, Andrew Putman
Answering a question of Farb-Leininger-Margalit, we give explicit lower bounds for the dilatations of pseudo-Anosov mapping classes lying in the kth term of the Johnson filtration…
Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=-1
Tara Brendle, Dan Margalit, Andrew Putman
We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of…
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).
The Torelli group and congruence subgroups of the mapping class group
Andrew Putman
These are the lecture notes for my course at the 2011 Park City Mathematics Graduate Summer School. The first two lectures covered the basics of the Torelli group and the Johnson h…
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…
Small generating sets for the Torelli group
Andrew Putman
Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup of the mapping class group has a finite generating set whose size grows cubically with respect to the genu…
Abelian quotients of subgroups of the mapping class group and higher Prym representations
Andrew Putman, Ben Wieland
A well-known conjecture asserts that the mapping class group of a surface (possibly with punctures/boundary) does not virtually surject onto if the genus of the surface is lar…
A Birman exact sequence for Aut(F_n)
Matthew B. Day, Andrew Putman
The Birman exact sequence describes the effect on the mapping class group of a surface with boundary of gluing discs to the boundary components. We construct an analogous exact seq…