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

Thomas W. Mattman

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arXiv · math/9911085

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

Thomas W. Mattman

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Abstract

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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BibTeX RIS

Thomas W. Mattman. 2001-08-08. The Culler-Shalen seminorms of the (-2,3,n) pretzel knot. https://arxiv.org/abs/math/9911085

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