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Real Regulators on Compact Complex Manifolds Open Access


Other title
Mathematics, Geometry, Regulators, K-Theory, Cohomology
Type of item
Degree grantor
University of Alberta
Author or creator
Kooistra, Remkes
Supervisor and department
Lewis, James (Mathematical and Statistical Sciences)
Examining committee member and department
Burgos Gil, Jose Ignacio (UAB Science Faculty)
Doran, Charles (Mathematical and Statistical Sciences)
Kuttler, Jochen (Mathematical and Statistical Sciences)
Chen, Xi (Mathematical and Statistical Sciences)
Page, Don (Physics)
Department of Mathematical and Statistical Sciences

Date accepted
Graduation date
Doctor of Philosophy
Degree level
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.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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