2013/05/07 by Taylor, Scott A.
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1305.1597
We survey aspects of classical combinatorial sutured manifold theory and show how they can be adapted to study exceptional Dehn fillings and 2-handle additions. As a consequence we show that if a hyperbolic knot β in a compact, orientable, hyperbolic 3-manifold M has the property that winding number and wrapping number are not equal with respect to a non-trivial class in H2(M,\boundary M), then, with only a few possible exceptions, every 3-manifold M' obtained by Dehn surgery on β with surgery distance Δ≥ 2 will be hyperbolic.