This thesis pursues the study of non-algebraic and non-Kahler compact complex manifolds by traditionally algebraic methods involving sheaves, cohomology and K-theory. To that end, Bott-Chern cohomology is developed to complement De Rham and Dolbeault cohomology. The first substantial chapter is devoted to the construction of Bott-Chern cohomology, including products. The next chapter is an investigation of Pic0(X) for non-Kahler complex manifolds. The next chapter uses line bundles represented by classes in this Pic0(X), along with Cartier divisors, to define a group of twisted cycle classes, generalizing a previous algebraic definition. On this group of twisted cycle classes, we use currents to construct a regulator map into Bott-Chern cohomology. Finally, in a chapter of conjectural statements and future directions, we explore the possibility of an alternate regulator using a cone complex of currents. We also conjecturally define a height pairing for certain kinds of compatible twisted cycle classes. / Mathematics
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/1677 |
| Date | 06 1900 |
| Creators | Kooistra, Remkes |
| Contributors | Lewis, James (Mathematical and Statistical Sciences), Doran, Charles (Mathematical and Statistical Sciences), Chen, Xi (Mathematical and Statistical Sciences), Kuttler, Jochen (Mathematical and Statistical Sciences), Page, Don (Physics), Burgos Gil, Jose Ignacio (UAB Science Faculty) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 594426 bytes, application/pdf |
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