1999/11/12 by Thomas W. Mattman, Mattman, Thomas W. · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25 #msc:57R65
paper · pdf · doi:10.48550/arxiv.math/9911085
34 pages, 11 figures; Results unchanged but major revision of logic and more detailed arguments
arxiv created 2001/08/08 · arxiv updated 2009/11/30
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.