Date of Award:
12-2009
Document Type:
Dissertation
Degree Name:
Doctor of Philosophy (PhD)
Department:
Mathematics and Statistics
Committee Chair(s)
Dariusz Wilczynski
Committee
Dariusz Wilczynski
Committee
Ian M. Anderson
Committee
LeRoy B. Beasley
Committee
Zhi-Qiang Wang
Committee
James T. Wheeler
Abstract
In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating the first Pontrjagin class for an arbitrary quaternionic toric 8-manifold.
Checksum
a84775b2e4c0b9ab0e5864c2c1f43542
Recommended Citation
Runge, Piotr, "A Comparison Theorem for the Topological and Algebraic Classification of Quaternionic Toric 8-Manifolds" (2009). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 501.
https://digitalcommons.usu.edu/etd/501
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