Exceptional surgery and boundary slopes

Masaharu Ishikawa, Thomas W. Mattman, Koya Shimokawa

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)807-821
ページ数15
ジャーナルOsaka Journal of Mathematics
43
4
出版ステータスPublished - 2006 12 1
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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