Exceptional surgery and boundary slopes

Details Exceptional surgery and boundary slopes Exceptional surgery and boundary slopes

2002-11-08

arxiv.org/abs/math/0211147v2

Mathematics

Geometric Topology

12 pages, 1 figure. Version 2 - minor revisions; corrected typos etc

Scientific paper

Let X be a norm curve in the SL(2,C)-character variety of a knot exterior M. Let t = || b || / || a || be the ratio of the Culler-Shalen norms of two distinct non-zero classes a, b in H_1(\partial M, Z). We demonstrate that either X has exactly two associated strict boundary slopes \pm t, or else there are strict boundary slopes r_1 and r_2 with |r_1| > t and |r_2| < t. As a consequence, we show that there are strict boundary slopes near cyclic, finite, and Seifert slopes. We also prove that the diameter of the set of strict boundary slopes can be bounded below using the Culler-Shalen norm of those slopes.

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