Now showing items 21-30 of 35
Failure of the Hasse Principle on General K3 Surfaces
(Oxford University Press, 2013)
We show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general K3 surface X of degree 2 over Q, together with a two-torsion Brauer class that is ...
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 ...
Hodge Theory and Lagrangian Planes on Generalized Kummer Fourfolds
(Independent University of Moscow, 2013)
Effective Computation of Picard Groups and Brauer-Manin Obstructions of Degree Two K3 Surfaces Over Number Fields
Using the Kuga-Satake correspondence we provide an effective algorithm for the computation of the Picard and Brauer groups of K3 surfaces of degree 2 over number fields.
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)
Filtering smooth concordance classes of topologically slice knots
We propose and analyze a structure with which to organize the difference between a knot in S3 bounding a topologically embedded 2–disk in B4 and it bounding a smoothly embedded disk. The n–solvable filtration of the ...
Knot Concordance and Homology Cobordism
(American Mathematical Society, 2013-06)
We consider the question: “If the zero-framed surgeries on two oriented knots in S3 are Z-homology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?” We show that this ...
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 ...