Off-campus UMass Amherst users: To download dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
Dirac maps and generalized complex geometry on homogeneous spaces
Generalized complex geometry  and, more generally, Dirac geometry , , unify several familiar geometric structures into one uniform viewpoint. In this thesis, we consider equivariant Dirac structures on homogeneous spaces as well as a new notion of morphisms between manifolds equipped with Dirac structures.^ We offer a description of equivariant Dirac structures on homogeneous spaces, which is then used to construct new examples of generalized complex structures. We consider Riemannian symmetric spaces, quotients of compact groups by closed connected subgroups of maximal rank, and nilpotent orbits in slnR . For each of these cases, we completely classify equivariant Dirac structures. Additionally, we consider equivariant Dirac structures on semisimple orbits in a semisimple Lie algebra. Here equivariant Dirac structures can be described in terms of root systems or by certain data involving parabolic subagebras.^ We provide two new notions of Dirac maps, giving two different Dirac categories. The first generalizes holomorphic and Poisson maps, while the second dual notion generalizes both symplectic and holomorphic maps. As an application, we consider Dirac groups (i.e. groups with Dirac structure such that group multiplication is a Dirac map). We explain the conditions under which a group with Dirac structure is a Dirac group. More precisely, we explain the data and conditions for a Dirac group. Dirac groups turn out to be a generalization of Poisson groups.^
"Dirac maps and generalized complex geometry on homogeneous spaces"
(January 1, 2008).
Electronic Doctoral Dissertations for UMass Amherst.