An odd-dimensional counterpart of generalized complex geometry

GAP Seminar

Meeting Details

For more information about this meeting, contact Ping Xu, Nigel Higson, Mathieu Stiénon.

Speaker: Aissa Wade, Penn State University

Abstract: In 2002, 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 $TM \oplus T^*M$. 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 contact, cosymplectic, and normal almost contact structures. Our new concept provide a natural framework for all these geometric objects on odd-dimensional manifolds. 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.

Room Reservation Information

Room Number: 106 McAllister

Date: 10/21/2014

Time: 2:30pm - 3:30pm