Singular milnor numbers of non-isolated matrix singularities
by Pike, Brian Adam, Ph.D., THE UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL, 2010, 197 pages; 3418732

Abstract:

In this dissertation we obtain formulas to describe the local topology of certain non-isolated matrix singularities. We find free divisors in various vector spaces of matrices which include the hypersurface of singular matrices as a component, and use these to express the singular Milnor numbers of matrix singularities in terms of the codimensions of groups of equivalences. On the spaces of symmetric and all n × n matrices, these free divisors arise through representations of finite dimensional solvable Lie groups; on the space of skew-symmetric matrices, we extend a finite-dimensional representation of a solvable Lie algebra to an infinite-dimensional one.

 
AdviserJames Damon
SchoolTHE UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
SourceDAI/B 71-09, p. , Sep 2010
Source TypeDissertation
SubjectsMathematics; Theoretical mathematics
Publication Number3418732
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