Abstract
<p> The A-polynomial of a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="3"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding="application/x-tex">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -manifold with toric boundary captures information about families of hyperbolic structures. We present an exposition of the theory of A-polynomials, including a characterization of their irreducible factors via torsion in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K 2"> <mml:semantics> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">K_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . Our previous work shows that the torsion locus and hence A-factor locus of the normal function associated with a family of smooth curves is finite, thus settling a conjecture of Antonin Guilloux and Julien Marché. We derive an additional finiteness result for A-factors by introducing the notion of overgenus. </p>