Now showing items 1-9 of 9
The Picard group of the moduli space of curves with level structures
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 divisibility properties of ...
The second rational homology group of the moduli space of curves with level structures
Let Γ be a finite-index subgroup of the mapping class group of a closed genus g surface that contains the Torelli group. For instance, Γ can be the level L subgroup or the spin mapping class group. We show that H2(Γ;Q) ∼= Q ...
Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=−1
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 hyperelliptic Torelli group can ...
Generating the Johnson filtration
(Mathematical Sciences Publishers, 2015)
For k≥1, let J1g(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≥1, there exists some Gk≥0 such that J1g(k) is generated ...
A Birman exact sequence for Aut(Fn)
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 sequence for the automorphism group of a free ...
Small generating sets for the Torelli group
(Mathematical Sciences Publisher, 2012)
Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup Ig of the genus g mapping class group has a finite generating set whose size grows cubically with respect to g. Our main tool is a new space called ...
The Rational Cohomology of the Mapping Class Group Vanishes in its Virtual Cohomological Dimension
(Oxford University Press, 2012)
The complex of partial bases for Fn and nite generation of the Torelli subgroup of Aut(Fn)
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 also prove that its ...
Abelian quotients of subgroups of the mapping class group and higher Prym representations
(London Mathematical Society, 2013-08)
A well-known conjecture asserts that the mapping class group of a surface (possibly with punctures/boundary) does not virtually surject onto Z if the genus of the surface is large. We prove that if this conjecture holds ...