UCLA

This thesis focuses on the classification of higher torsion invariants, which are invariants of smooth structures on manifold bundles. There are many different definitions of these invariants using methods ranging from analytic calculations to Morse theory to homotopy theory. The comparison of the different definitions is facilitated by an axiomatic approach developed by K. Igusa and the author. We survey the different definitions of higher torsion and their classification, and provide a detailed account of the example of higher twisted smooth torsion and its compliance with the axioms.