Mathematics – Geometric Topology
Scientific paper
2001-02-06
Proc. of Knot Theory - dedicated to Prof. Murasugi (Univ. of Toronto '99) (2000) 212-218
Mathematics
Geometric Topology
7 pages, 3 figures
Scientific paper
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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