Ping Xu, Dissertation Advisor/Co-Advisor Ping Xu, Committee Chair/Co-Chair Mathieu Philippe Stienon, Committee Chair/Co-Chair Aissa Wade, Committee Member Adrian Ocneanu, Committee Member Luen Chau Li, Committee Member Martin Bojowald, Committee Member
Keywords:
Courant algebroid cohomology matched pairs
Abstract:
We introduce Courant algebroids, providing definitions, some historical notes,
and some elementary properties. Next, we summarize basic properties of graded manifolds. Then, drawing on the work by Roytenberg and others, we introduce the graded or supergraded language demostrating a cochain complex/ cohomology for (general) Courant algebroids. We review spectral sequences and show how this tool is used to compute cohomology for regular
Courant algebroids with a split base. Finally we analyze matched pairs of Courant algebroids including the complexified standard Courant algebroid of a complex manifold and the matched pair arising from a holomorphic Courant
algebroid.
