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## Cutting and pasting in the Torelli group

- Andrew Putman
- Mathematics
- 15 August 2006

We introduce machinery to allow “cut-and-paste”-style inductive arguments in the Torelli subgroup of the mapping class group. In the past these arguments have been problematic because restricting the… Expand

## On the Fukaya Categories of Higher Genus Surfaces

- Andrew Putman, P. Seidel
- Mathematics
- 2006

We construct the Fukaya category of a closed surface equipped with an area form using only elementary (essentially combinatorial) methods. We also compute the Grothendieck group of its derived… Expand

## Stability in the homology of congruence subgroups

- Andrew Putman
- Mathematics
- 23 January 2012

The homology groups of many natural sequences of groups $$\{G_n\}_{n=1}^{\infty }$${Gn}n=1∞ (e.g. general linear groups, mapping class groups, etc.) stabilize as $$n \rightarrow \infty $$n→∞. Indeed,… Expand

## The Johnson homomorphism and its kernel

- Andrew Putman
- Mathematics
- 2 April 2009

We give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel of the Johnson homomorphism on the Torelli subgroup of the mapping class group is generated by separating… Expand

## The Picard group of the moduli space of curves with level structures

- Andrew Putman
- Mathematics
- 4 August 2009

For 4 L and g large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level L structures. In particular, we determine the… Expand

## Representation stability and finite linear groups

- Andrew Putman, Steven V. Sam
- Mathematics
- 16 August 2014

We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties… Expand

## Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at $$t=-1$$t=-1

- Tara E. Brendle, D. Margalit, Andrew Putman
- Mathematics
- 16 November 2012

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 Hain. The… Expand

## An Infinite Presentation of the Torelli Group

- Andrew Putman
- Mathematics
- 19 March 2007

In this paper, we construct an infinite presentation of the Torelli subgroup of the mapping class group of a surface whose generators consist of the set of all “separating twists”, all “bounding pair… Expand

## The complex of partial bases for Fn and finite generation of the Torelli subgroup of Aut (Fn)

- M. Day, Andrew Putman
- Mathematics
- 9 December 2010

We study the complex of partial bases of a free group, which is an analogue for Aut(Fn) of the curve complex for the mapping class group. We prove that it is connected and simply connected, and we… Expand

## A note on the connectivity of certain complexes associated to surfaces

- Andrew Putman
- Mathematics
- 26 December 2006

This note is devoted to a trick which yields almost trivial proofs that certain complexes associated to topological surfaces are connected or simply connected. As an application, we give new proofs… Expand

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