Date of Award
8-2013
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Dr. Jeffrey Strom
Second Advisor
Dr. John Martino
Third Advisor
Dr. David Richter
Fourth Advisor
Dr. John Oprea
Keywords
category sequence, rational realizability, Lusternik-Schnirelmann
Abstract
The Lusternik-Schnirelmann (or LS) category of a space is one less than the number of contractible open sets with which we can cover the space. If we look at the LS categories of the skeleta of a CW complex, we find a sequence of dimensions where the LS category changes. I discuss whether certain of these "category sequences" (defined in the paper, "Categorical Sequences", by Nendorf, Scoville, and Strom) could be realized as the categorical sequences of rational spaces. I first reduce from looking at all rational spaces to only Postnikov sections of finite wedges of spheres. Using the Leray-Serre Spectral Sequence, I show that certain sequences can be rationally realized with a Postnikov section of a wedge of enough spheres. I finally conjecture that these are the only sequences in this pattern to be rationally realizable.
Access Setting
Dissertation-Open Access
Recommended Citation
Houck, Julie Dare, "A Pattern in the Lusternik-Schnirelmann Category of Rational Spaces" (2013). Dissertations. 181.
https://scholarworks.wmich.edu/dissertations/181