105 citations · 705 across the 54 of their papers we have counts for
55 papers
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…
Word length versus lower central series depth for surface groups and RAAGs
Justin Malestein, Andrew Putman
For surface groups and right-angled Artin groups, we prove lower bounds on the shortest word in the generators representing a nontrivial element of the kth term of the lower centra…
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 stable cohomology of the moduli space of curves with level structures
Andrew Putman
We prove that in a stable range, the rational cohomology of the moduli space of curves with level structures is the same as that of the ordinary moduli space of curves.
The free factor complex and the dualizing module for the automorphism group of a free group
Zachary Himes, Jeremy Miller, Sam Nariman +1
Answering a question of Hatcher-Vogtmann, we prove that the top homology group of the free factor complex is not the dualizing module for , at least for .
A new approach to twisted homological stability, with applications to congruence subgroups
Andrew Putman
We introduce a new method for proving twisted homological stability, and use it to prove such results for symmetric groups and general linear groups. In addition to sometimes sligh…
The Steinberg representation is irreducible
Andrew Putman, Andrew Snowden
We prove that the Steinberg representation of a connected reductive group over an infinite field is irreducible. For finite fields, this is a classical theorem of Steinberg and Cur…
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}…
VIC-modules over noncommutative rings
Andrew Putman, Steven V Sam
For a finite ring , not necessarily commutative, we prove that the category of -modules over a left Noetherian ring is locally Noetherian, generalizi…
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…
On the top dimensional cohomology groups of congruence subgroups of
Jeremy Miller, Peter Patzt, Andrew Putman
Let be the level- principal congruence subgroup of . Borel-Serre proved that the cohomology of vanishes above degree . W…
The dualizing module and top-dimensional cohomology group of
Andrew Putman, Daniel Studenmund
For a number ring , Borel and Serre proved that is a virtual duality group whose dualizing module is the Steinberg module. They also proved…
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…
Stability in the homology of unipotent groups
Andrew Putman, Steven V Sam, Andrew Snowden
Let be a (not necessarily commutative) ring whose additive group is finitely generated and let be the group of upper-triangular unipotent matrices over…
On finite generation of the Johnson filtrations
Thomas Church, Mikhail Ershov, 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 is finit…
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…
Homological vanishing for the Steinberg representation
Avner Ash, Andrew Putman, Steven V Sam
For a field , we prove that the th homology of the groups , , , , and with coefficients in their Steinberg represen…
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…