A Comparison Theorem for the Topological and Algebraic Classification of Quaternionic Toric 8-Manifolds

• Main Author: Runge, Piotr
• Format: Others
• Published: DigitalCommons@USU 2009
• Subjects: 8-manifold; algebra; quaternionic; topology; toric; Algebra
• Online Access: https://digitalcommons.usu.edu/etd/501; https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1497&context=etd

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.