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arXiv math/01020492001-02-06math.GT

The Culler-Shalen seminorms of the (-3,3,4) pretzel knot

Thomas W. Mattman

备注：: 7 pages, 3 figures
发表信息：: Proc. of Knot Theory - dedicated to Prof. Murasugi (Univ. of Toronto '99) (2000) 212-218

英文摘要：

We describe a method to compute the Culler-Shalen seminorms of a knot, using the (-3,3,4) pretzel knot as an illustrative example. We deduce that the SL2(C)-character variety of this knot consists of three algebraic curves and that it admits no non-trivial cyclic or finite surgeries. We also summarize similar results for other (-3,3,n) pretzel knots including the observation that the Seifert surgeries for these knots are precisely those integral slopes lying between two of the boundary slopes.

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