Singular Milnor numbers of non-isolated matrix singularities Public Deposited

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Last Modified
  • March 21, 2019
Creator
  • Pike, Brian Adam
    • Affiliation: College of Arts and Sciences, Department of Mathematics
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 times 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.
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  • In Copyright
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  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics."
Advisor
  • Damon, James
Degree granting institution
  • University of North Carolina at Chapel Hill
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Place of publication
  • Chapel Hill, NC
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  • Open access
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