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


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.

Access Setting

Dissertation-Open Access

Included in

Mathematics Commons