Date Available
5-8-2014
Year of Publication
2014
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dr. Serge Ochanine
Abstract
This dissertation demonstrates a procedure to view any quasitoric manifold as a “minimal” sub-manifold of an ambient quasitoric manifold of codimension two via the wedge construction applied to the quotient polytope. These we term wedge quasitoric manifolds. We prove existence utilizing a construction on the quotient polytope and characteristic matrix and demonstrate conditions allowing the base manifold to be viewed as dual to the first Chern class of the wedge manifold. Such dualization allows calculations of KO characteristic classes as in the work of Ochanine and Fast. We also examine the Todd genus as it relates to two types of wedge quasitoric manifolds. Background matter on polytopes and toric topology, as well as spin and complex cobordism are provided.
Recommended Citation
Hines, Clinton M., "Spin Cobordism and Quasitoric Manifolds" (2014). Theses and Dissertations--Mathematics. 17.
https://uknowledge.uky.edu/math_etds/17
