Exceptional surgery and boundary slopes

Masaharu Ishikawa, Thomas W. Mattman, Koya Shimokawa

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Abstract

Let X be a norm curve in the SL(2, ℂ)-character variety of a knot exterior M. Let t = ||β||/||α|| be the ratio of the Culler-Shalen norms of two disαtinct non-zero classes α,β ∈ H 1(∂M,Z). We demonstrate that either X has exactly two associated strict boundary slopes ±t, or else there are strict boundary slopes r1 and r2 with |r1| > t and |r2| < 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.

Original languageEnglish
Pages (from-to)807-821
Number of pages15
JournalOsaka Journal of Mathematics
Volume43
Issue number4
Publication statusPublished - 2006 Dec 1
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Ishikawa, M., Mattman, T. W., & Shimokawa, K. (2006). Exceptional surgery and boundary slopes. Osaka Journal of Mathematics, 43(4), 807-821.