Wednesday, October 29th, 2014
3:30pm - 4:30pm, in Science 2-066

Aissa Wade

Penn State University

An odd-dimensional counterpart of generalized complex geometry

Abstract: Fourteen years ago, Hitchin introduced the theory of generalized complex structures which has been developed since then. Generalized complex structures on an even-dimensional manifold M are generalizations of symplectic and complex structures on M. More precisely, any generalized complex structure on M can be viewed as a complex structure on the vector bundle TM+T*M. After a brief review of generalized complex geometry, we will discuss its odd-dimensional counterpart. The odd-dimensional analogues of generalized complex structures are called generalized contact structures. They include both contact and cosymplectic structures and provide a natural framework for these geometric objects. However, there is a sharp contrast with generalized complex geometry. Non-trivial examples can be constructed using a Boothby-Wang construction type.This is a joint work with Yat Sun Poon.