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Stavros Garoufalidis and Thomas W. Mattman
The A-polynomial of the (-2,3,3+2n) pretzel knots view print
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| Published: |
April 11, 2011 |
| Keywords: |
Pretzel knots, A-polynomial, Newton polygon, character variety, Culler-Shalen seminorm, holonomic sequences, quasi-polynomials. |
| Subject: |
Primary 57N10. Secondary 57M25 |
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Abstract
We show that the A-polynomial An of the 1-parameter family of pretzel
knots Kn=(-2,3,3+2n) satisfies a linear recursion relation of order 4 with
explicit constant coefficients and initial conditions. Our proof combines
results of Tamura-Yokota and the second author. As a corollary, we show
that the A-polynomial of Kn and the mirror of K-n are related
by an explicit GL(2,Z)
action. We leave open the question of whether or not
this action lifts to the quantum level.
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| Acknowledgements
The first author was supported in part by the NSF
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| Author information
Stavros Garoufalidis:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
stavros@math.gatech.edu
Thomas W. Mattman:
Department of Mathematics and Statistics, California State University, Chico, Chico, CA 95929-0525, USA
TMattman@CSUChico.edu
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