Singular Milnor numbers of non-isolated matrix singularities
Public Deposited- 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.
- Date of publication
- August 2010
- DOI
- Resource type
- Rights statement
- In Copyright
- Note
- "... 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
- Language
- Publisher
- Place of publication
- Chapel Hill, NC
- Access right
- Open access
- Date uploaded
- March 18, 2013
Relations
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