arXiv subjects
Publications and source records attributed to Steve Boyer.
We show that the nonzero roots of the torsion polynomials associated to the infinite cyclic covers of a given compact, connected, orientable 3-manifold M are contained in a compact part of the complex plane a priori determined by M. This result is applied to prove that when M is closed, it dominates at most finitely many Sol manifolds.
It is conjectured that for each knot $K$ in $S^3$, the fundamental group of its complement surjects onto only finitely many distinct knot groups. Applying character variety theory we obtain an affirmative solution of the conjecture for a class of small knots that includes 2-bridge knots.
We give new bounds for the distance between two exceptional filling slopes for a 1-cusped hyperbolic 3-manifold in several different situations. The distance between a reducible slope and a slope that produces a manifold with finite fundamental group is at most 2. The distance between a reducible slope and one that produces a very small manifold is also at most 2. The distance between a reducible slope and one which produces a manifold with a pi_1 injective torus is at most 4. The methods used involve both characteristic submanifold theory and the theory of the PSL(2,C) character variety.