On Strict Higher Categories and their Application to Cobordism Theory
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The main goal of the present thesis is an exposition of the Bökstedt-Madsen theorem (), 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.  M. Bökstedt and Ib Madsen, "The cobordism category and Waldhausen's K-theory"