Bass, D. W. (1975) The topological classification of endomorphisms of vector bundles. PhD thesis, University of Warwick.

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Abstract

I have made an attempt in this thesis at a systematic topological classification of the endomorphisms of a vector bundle . Chapter one provides the motivation for such a classification and for the notions of 'local' and 'global' topological equivalence of bundle endomorphisms that are given in Chapter 2. Both the local and global classification problems turned out to be a great deal more difficult than anticipated. A complete local and global classification of the generic endomorphisms of real and complex line bundles over a smooth manifold is given in Chapter 2. For real plane bundles, the local classification problem is partly solved, but no attempt is made at the global problem. Chapter 3 gives the complete local classification for generic endomorphisms that have bifurcations of codimension one. Finally in Chapter 4 an attempt is made at the codimensions two and four local classification problems. Only partial results and conjectures are offered. Other notions of local equivalence are suggested.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Endomorphisms (Group theory), Vector bundles, Topology
Official Date:	July 1975
Dates:	Date Event July 1975 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Schwarzenberger, R. L. E.
Sponsors:	Memorial University of Newfoundland
Extent:	98 leaves : illustrations
Language:	eng

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