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Title: Characteristic classes and projective modules
Author: Thomas, Alan David
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1970
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This thesis is in 4 separate parts, of which Chapters 1 and 2. form the first part, and Chapters 3,4,5 are the remaining parts. The thesis is concerned with characteristic classes, which can be viewed as obstructions to stable triviality. In C:lapter 1 we show just how much information the Chern classes carry in this respect, by proving that they determine th0 stable class up to a finite set. Chapter 3 discusses Chern classes of vector bundles over suspensions, and the effect on Chern classes of collapsing bundles. In Chapter 5 we introduce characteristic classes into algebraic K-theory and show that these have analogous properties to topological characteristic classes, in particular that the first characteristic class is a complete invariant for projective modules of rank 1. Chapter 2 concerns the topological process of blowing up a submanifold and the effect on characteristic classes. For this chapter we need to understand the theory of orientation, umkehr homomorphisms and Riemann-Roch theorems, and this is described in a fairly abstract sense in Chapter 1. Chapter 4 shows how the trace of an endomorphism (which in special cases can be considered as a first characteristic class) can be axiomatized, and proves the existence and uniqueness of a trace under certain finiteness conditions on the category.
Supervisor: Not available Sponsor: Science Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics