Real Regulators on Compact Complex Manifolds

• Author / Creator

  Kooistra, Remkes

• 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.

• Subjects / Keywords

  • Mathematics
  • Geometry
  • Regulators
  • K-Theory
  • Cohomology

• Graduation date

  Spring 2011

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R39D7F

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.