The Culler-Shalen seminorms of the (-2,3,n) pretzel knot

Details The Culler-Shalen seminorms of the (-2,3,n) pretzel knot The Culler-Shalen seminorms of the (-2,3,n) pretzel knot

1999-11-12

arxiv.org/abs/math/9911085v3

Mathematics

Geometric Topology

34 pages, 11 figures; Results unchanged but major revision of logic and more detailed arguments

Scientific paper

We show that the SL(2,C)-character variety of the (-2,3,n) pretzel knot consists of two (respectively three) algebraic curves when 3 does not divide n (respectively 3 divides n) and give an explicit calculation of the Culler-Shalen seminorms of these curves. Using this calculation, we describe the fundamental polygon and Newton polygon for these knots and give a list of Dehn surgeries yielding a manifold with finite or cyclic fundamental group. This constitutes a new proof of property P for these knots.

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