Now showing items 1-20 of 81

• #### 4-Manifolds With Inequivalent Symplectic Forms and 3-Manifolds With Inequivalent Fibrations ﻿

(International Press, 1999)
We exhibit a closed, simply connected 4-manifold $X$ carrying two symplectic structures whose ﬁrst Chern classes in $H^2 (X, \mathbb{Z})$ lie in disjoint orbits of the diffeomorphism group of $X$. Consequently, the ...
• #### The Alexander Polynomial of a 3-Manifold and the Thurston Norm on Cohomology ﻿

(Elsevier, 2002)
Let M be a connected, compact, orientable 3-manifold with $b_1(M)>1$, whose boundary (if any) is a union of tori. Our main result is the inequality ${\parallel \phi \parallel}_A \le {\parallel \phi \parallel}_T$ between ...
• #### Amenability, Poincaré Series and Quasiconformal Maps ﻿

(Springer Verlag, 1989)
Any covering $Y \rightarrow X$ of a hyperbolic Riemann surface$X$ of finite area determines an inclusion of Teichmüller spaces $Teich(X) \hookrightarrow Teich(Y)$. We show this map is an isometry for the Teichmüller ...
• #### Amenable Coverings of Complex Manifolds and Holomorphic Probability Measures ﻿

(Springer Verlag, 1992)
• #### Area and Hausdorff Dimension of Julia Sets of Entire Functions ﻿

(American Mathematical Society, 1987)
We show the Julia set of $\lambda\sin(z)$ has positive area and the action of $\lambda\sin(z)$ on its Julia set is not ergodic; the Julia set of $\lambda\exp(z)$ has Hausdorff dimension two but in the presence of ...
• #### Automorphisms of Even Unimodular Lattices and Unramified Salem Numbers ﻿

(Elsevier, 2002)
In this paper we study the characteristic polynomials $S(x)=\det(xI−F| II_{p,q})$ of automorphisms of even unimodular lattices with signature $(p,q)$. In particular, we show that any Salem polynomial of degree $2n$ ...
• #### Automorphisms of projective K3 surfaces with minimum entropy ﻿

(Springer Science + Business Media, 2015)
• #### Automorphisms of Rational Maps ﻿

(Springer, 1988)
• #### Billiards and Hilbert Modular Surfaces ﻿

(Max-Planck Institut, 2003)
• #### Billiards and Teichmüller Curves on Hilbert Modular Surfaces ﻿

(American Mathematical Society, 2003)
This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian ...
• #### Braid Groups and Hodge theory ﻿

(Springer, 2012)
This paper gives an account of the unitary representations of the braid group that arise via the Hodge theory of cyclic branched coverings of $\mathbb{P}^1$ , highlighting their connections with ergodic theory, complex ...
• #### Braiding of the Attractor and the Failure of Iterative Algorithms ﻿

(Springer Verlag, 1988)
• #### Cascades in the Dynamics of Measured Foliations ﻿

(Elsevier Masson, 2014-03-14)
• #### The Classification of Conformal Dynamical Systems ﻿

(International Press, 1995)
• #### A Compactification of the Space of Expanding Maps on the Circle ﻿

(Springer Verlag, 2009)
We show the space of expanding Blaschke products on $S1$ is compactified by a sphere of invariant measures, reminiscent of the sphere of geodesic currents for a hyperbolic surface. More generally, we develop a dynamical ...
• #### Complex Earthquakes and Teichmuller Theory ﻿

(American Mathematical Society, 1998)
It is known that any two points in Teichmuller space are joined by an earthquake path. In this paper we show any earthquake path $\mathbb{R} \rightarrow T(S)$ extends to a proper holomorphic mapping of a simplyconnected ...
• #### The complex geometry of Teichmüller space ﻿

(2014-06-06)
We study isometric maps between Teichmüller spaces and bounded symmetric domains in their Kobayashi metric. We prove that every totally geodesic isometry from a disk to Teichmüller space is either holomorphic or anti-holomorphic; ...
• #### Coxeter Groups, Salem Numbers and the Hilbert Metric ﻿

(Springer Verlag, 2002)
• #### Cubic curves and totally geodesic subvarieties of moduli space ﻿

(Annals of Mathematics, Princeton U, 2017)
In this paper we present the first example of a primitive, totally geodesic subvariety F⊂g,nF⊂Mg,n with dim(F)>1dim(F)>1. The variety we consider is a surface F⊂1,3F⊂M1,3 defined using the projective geometry of plane ...
• #### Cusps are Dense ﻿

(Princeton University Press, 1991)
We show cusps are dense in Bers' boundary for Teichmuller space. The proof rests on an estimate for the algebraic effect of a unit quasiconformal deformation supported in the thin part of the Riemann surface.