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Summary: THE A-POLYNOMIAL HAS ONES IN THE CORNERS
D. COOPER AND D. D. LONG
1. Definition of the A-polynomial
The A-polynomial was introduced in [3] (see also [5]), and we present an
alternative definition here. Let M be a compact 3-manifold with boundary a torus T.
Pick a basis , µ of
"
T, which we shall refer to as the longitude and meridian.
Consider the subset RU
of the affine algebraic variety R l Hom (
"
M, SL
#
) having
the property that () and (µ) are upper triangular. This is an algebraic subset of R,
since one just adds equations stating that the bottom-left entries in certain matrices
are zero. There is a well-defined eigenvalue map
(iµ ): RU
,- #
given by taking the top-left entries of () and (µ). Thus the closure of the image
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