Ptolemy coordinates, Dehn invariant, and the A-polynomial
Christian K. Zickert
TL;DR
This paper introduces a new method for computing A-polynomials and A-varieties using Ptolemy coordinates for a broader class of representations, and provides a formula for the Dehn invariant of SL(n,C)-representations.
Contribution
It extends Ptolemy coordinates to non-boundary-unipotent representations, enabling new algorithms for A-polynomial and A-variety computations, and derives a Dehn invariant formula.
Findings
New algorithm for SL(2,C) A-polynomial computation
Extension of Ptolemy coordinates to non-boundary-unipotent cases
Formula for Dehn invariant of SL(n,C)-representations
Abstract
We define Ptolemy coordinates for representations that are not necessarily boundary-unipotent. This gives rise to a new algorithm for computing the SL(2,C) A-polynomial, and more generally the SL(n,C) A-varieties. We also give a formula for the Dehn invariant of an SL(n,C)-representation.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory