Steve Morris
Ph.D. (2006) Cornell University

First Position

Escobar Assistant Professor, Cornell University

Dissertation

Four- and Six-Dimensional Nilmanifolds and Symplectic Forms

Advisor: Reyer Sjamaar
Research Area:Symplectic Topology

Abstract: In this thesis we study four- and six-dimensional nilmanifolds using their associated rational Lie algebras and minimal models. We show that all four-dimensional nilmanifolds have symplectic structures. We then show that there exists a family of four-dimensional nilmanifolds, non diffeomorphic to the Kodaira-Thurston manifold, which fibrate symplectically as torus bundles over tori. Using similar methods we also investigate which six-dimensional nilmanifolds possess symplectic structures. Our last result concerns symplectic torus actions. We show that the Duistermaat-Heckman function defined on a torus is a piecewise trignometric polynomial. We present examples of torus valued moment maps on a family of symplectic manifolds studied by Cordero, Fernandez and Gray.

Last modified: October 31, 2006