Abstracts of Talks at the Cornell Topology Festival, May 3-5, 2002

MLADEN BESTVINA

MEASURED  LAMINATIONS  AND  GROUP  THEORY

Abstract not available.

DANIEL BISS

THE  COMBINATORICS  OF  SMOOTH  MANIFOLDS:  ORIENTED  MATROIDS  IN  TOPOLOGY

The problem of finding a combinatorial formula for the rational Pontrjagin classes was solved in the early 90's by Gelfand and MacPherson; their solution makes essential use of combinatorial objects called oriented matroids. We show that the oriented matroids in question actually determine the tangent bundle of a smooth manifold; we will also discuss potiential applications of this result to the topology of diffeomorphism groups.

STEVE GERSTEN

ISOPERIMETRIC  INEQUALITIES  FOR  NILPOTENT  GROUPS

This is joint research with D. F. Holt and T. R. Riley.

 

We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function.

 

Paper reference: arXiv:math.GR/0201261

DUSA McDUFF

THE  TOPOLOGY  OF  GROUPS  OF  SYMPLECTOMORPHISMS

A symplectomorphism is a diffeomorphism of a manifold that preserves a symplectic form. Ever since Gromov showed that the group of symplectomorphisms of the product of two 2-spheres of equal size has the homotopy type of an extension of SO(3) x SO(3) by Z/2Z, people have been interested in understanding the special properties of groups of symplectomorphisms. This survey talk will describe some ways in which the structure of a group of symplectomorphisms differs from that of an arbitrary diffeomorphism group.

YAIR MINSKY

ON  THURSTON'S  ENDING  LAMINATION  CONJECTURE

The classification theory of hyperbolic 3-manifolds (with finitely generated fundamental group) hinges on Thurston's conjecture from the late 70's, that such a manifold is uniquely determined by its topological type and a finite number of invariants that describe the asymptotic structure of its ends.

 

We will describe the recent proof of this conjecture, in the "incompressible boundary case", in joint work with J. Brock and R. Canary.

PETER OZSVATH

HOLOMORPHIC  DISKS  AND  LOW-DIMENSIONAL  TOPOLOGY

I will discuss recent work with Zoltan Szabo, in which we use techniques from symplectic geometry -- holomorphic disks, and Lagrangian Floer homology -- to construct topological invariants for three-and four-manifolds. These invariants yield many of the four-dimensional results which have been proved using their gauge-theoretic predecessors (Donaldson-Floer and Seiberg-Witten theory), though the new invariants are constructed using more topological and combinatorial input, rendering them easier to calculate. I hope to focus on some of their applications to three-dimensional topological questions which have not been addressed by gauge theory.

GUOLIANG YU

THE  NOVIKOV  CONJECTURE  AND  GEOMETRY  OF  GROUPS

I will explain what is the Novikov conjecture, why it is interesting and how it is related to geometry of groups.

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