On Strict Higher Categories and their Application to Cobordism Theory
Master thesis
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http://hdl.handle.net/11250/2352689Utgivelsesdato
2015Metadata
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Sammendrag
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"