Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Jeffrey Strom

Second Advisor

Dr. John Martino

Third Advisor

Dr. David Richter

Fourth Advisor

Dr. John Oprea


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

Included in

Mathematics Commons