Geometric category, LS-category and strong category : an overview

Details

Supervisors

Gran, Marino ; Parent, Paul-Eugène

Faculty

Faculté des sciences

Degree label

Master [120] en sciences mathématiques, à finalité approfondie

Abstract

The goal of this thesis is to familiarize ourselves with specific homotopy invariants. In the first two chapters, we establish the foundation for the subsequent chapters by introducing the categories in which we will work, with an emphasis on understanding how pullbacks and pushouts operate within each of these categories. Moving on to the second part, we will introduce the objects of main interest, starting with the geometric category. We then apply this new notion to the objects discussed in the first two chapters and prove that it is not a homotopy invariant. This raises questions about how we can obtain a homotopic invariant, which leads to the definitions of LS-category and strong category. These definitions appear to be homotopy invariants. In the last two chapters, we explore additional definitions and properties of the LS-category and the strong category.