Now showing items 11-20 of 35
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 ...
Log minimal model program for the moduli space of stable curves: the first flip
(Department of Mathematics, Princeton University, 2013)
We give a geometric invariant theory (GIT) construction of the log canonical model M¯g(α) of the pairs (M¯g,αδ) for α∈(7/10–ϵ,7/10] for small ϵ∈Q+. We show that M¯g(7/10) is isomorphic to the GIT quotient of the Chow variety ...
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 ...
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 ...
Dichotomy for arithmetic progressions in subsets of reals
(American Mathematical Society, 2016)
Let H stand for the set of homeomorphisms φ:[0, 1] → [0, 1]. We prove the following dichotomy for Borel subsets A ⊂ [0, 1]: • either there exists a homeomorphism φ ∈ Hsuch that the image φ(A) contains no 3-term arithmetic ...
Cocycle rigidity and splitting for some discrete parabolic actions
(American Institute of Mathematical Sciences, 2014)