Hayden, John (1980) Some global properties of singularities. PhD thesis, University of Warwick.

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Abstract

We use the techniques of algebraic topology to study singularities. We first generalise the Thom polynomial theorem to apply to parametrised maps. We then give a detailed study of the singularities of parametrised real valued functions, with applications to the extension of locally stable maps and Lagrangian inmersions. Secondly we use the geometric interpretation of the cohomology theory associated to the Thom spectrum M3 given by Quillen, to represent a given singularity set by a cobordism class. We prove a theorem analogous to the Thom polynomial theorem valid for unoriented cobordism theory.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Algebraic topology, Cohomology operations, Singularities (Mathematics)
Official Date:	1980
Dates:	Date Event 1980 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Extent:	79, 8 leaves : illustrations
Language:	eng

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