On Iwase's Construction of a Counterexample to Ganea's Conjecture

Abstract

In 1971, Ganea put forth a conjecture that the LS category of the Cartesian product of a topological space X with a sphere Sn is always exactly 1 higher than the LS category of X by itself. Several special cases of this conjecture were proven in the years following, however the question remained open until 1998 when Iwase produced not just one, but infinitely many counterexamples. In this thesis, we study the methods implemented by Iwase, culminating in the construction of his counterexample.