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Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2016
Month Degree Awarded
September
First Advisor
Alexei Oblomkov
Subject Categories
Algebraic Geometry
Abstract
We conjecture a relationship between the Hilbert schemes of points on a singular plane curve and the Kauffman invariant of the link associated to the singularity. Specifcally, we conjecture that the generating function of certain weighted Euler characteristics of the Hilbert schemes is given by a normalized specialization of the difference between the Kauffman and HOMFLY polynomials of the link. We prove the conjecture for torus knots. We also develop some skein theory for computing the Kauffman polynomial of links associated to singular points on plane curves.
DOI
https://doi.org/10.7275/8997645.0
Recommended Citation
Shelly, Thomas, "Skein Theory and Algebraic Geometry for the Two-Variable Kauffman Invariant of Links" (2016). Doctoral Dissertations. 804.
https://doi.org/10.7275/8997645.0
https://scholarworks.umass.edu/dissertations_2/804