Exceptional surgery and boundary slopes

Thomas Mattman

KNOTS in WASHINGTON XV (2nd Japan-USA Workshop in Knot Theory)
January 10-15, 2003
George Washington University and Johns Hopkins University
Washington, DC and Baltimore, MD, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Shin-ichi Suzuki, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

Conference Homepage

Exceptional surgery and boundary slopes
by
Thomas Mattman
California State University, Chico
Coauthors: Masaharu Ishikawa (Tokyo Metropolitan University, Japan), Koya Shimokawa (Saitama University, Japan)

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( M, Z). We demonstrate that either X has exactly two associated strict boundary slopes, t and -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.

Date received: November 29, 2002