Date of Award
Doctor of Philosophy
Dr. Jeffrey Strom
Dr. John Martino
Dr. David Richter
Dr. John Oprea
category sequence, rational realizability, Lusternik-Schnirelmann
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.
Houck, Julie Dare, "A Pattern in the Lusternik-Schnirelmann Category of Rational Spaces" (2013). Dissertations. 181.