Now showing items 1-10 of 39
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 ...
Higher-Order Signature Cocycles for Subgroups of Mapping Class Groups and Homology Cylinders
(Oxford University Press, 2012)
Homology cobordism and Seifert fibered 3-manifolds
(American Mathematical Society, 2014)
It is known that every closed oriented 3-manifold is homology cobordant to a hyperbolic 3-manifold. By contrast we show that many homology cobordism classes contain no Seifert fibered 3-manifold. This is accomplished by ...
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 ...
Wigner-von Neumann type perturbations of periodic Schrödinger operators
(American Mathematical Society, 2015)
Schrödinger operators on the half line. More precisely, the perturbations we consider satisfy a generalized bounded variation condition at infinity and an LP decay condition. We show that the absolutely continuous spectrum ...
Cubic fourfolds containing a plane and a quantic del Pezzo surface
(Foundation Compositio Mathematica, 2014)
We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontriviality of the Brauer class β of the even ...
New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains
(American Physical Society, 2014)
We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson (LR) bound for an isotropic XY chain in a quasiperiodic transversal magnetic field. Instead of the usual effective light ...
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 ...
The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian
We consider the density of states measure of the Fibonacci Hamiltonian and show that, for small values of the coupling constant V , this measure is exact-dimensional and the almost everywhere value dV of the local ...