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Characteristic classes and projective modules
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Thomas, A. D. (1970) Characteristic classes and projective modules. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1733083~S1
Abstract
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.
| Item Type: | Thesis (PhD) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Characteristic classes, Projective modules (Algebra), Mathematics, Fiber bundles (Mathematics), K-theory | ||||
| Official Date: | 1970 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Schwarzenberger, R. L. E. | ||||
| Sponsors: | Science Research Council (Great Britain) | ||||
| Extent: | 152 leaves | ||||
| Language: | eng |
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