On Strict Higher Categories and their Application to Cobordism Theory

Abstract

The main goal of the present thesis is an exposition of the Bökstedt-Madsen theorem ([1]), which relates the classifying space of the embedded cobordism category to certain iterated loop spaces of the Thom space of universal vector bundles. To this end, we first give a brief exposition of higher category theory with emphasis on the k-fold categories and a general introduction to cobordism theory and moduli spaces of manifolds. In the final chapter, we explore the extension of the theory to accommodate manifolds with Baas-Sullivan singularities.

[1] M. Bökstedt and Ib Madsen, "The cobordism category and Waldhausen's K-theory"