Sponsored by Elizabethtown College, Franklin and Marshall College, Lebanon Valley College, and Millersville University
12 September David Lyons, Lebanon Valley College 3 October David Johnson, Lehigh University 7 November Josh Sabloff, Haverford College 5 December Vincent Coll, Lehigh University 6 February Lisa Traynor, Bryn Mawr College 6 March RESCHEDULED! Zhigang Han, Millersville University 10 April Barbara Nimershiem, Franklin and Marshall College 1 May Zhigang Han, Millersville UniversityTGTS meets at 4:30 p.m. on the first Friday of each month. The public is cordially invited to attend.
Date: 10 April 2015, 4:30pm Location: Hempfield High School, Room 213 Speaker: Barbara Nimershiem, Franklin and Marshall College Title: Cellular decompositions of hyperbolic 3-manifolds Abstract. Bill Thurston's work (c. 1980) shows us that almost all knots have hyperbolic complements. (The exceptions---torus knots and satellite knots---are well understood.) The same is true for non-split links. His proofs are constructive: first decompose a link complement into two ideal polyhedra identified along their boundaries and then put an appropriate hyperbolic structure on the polyhedra. While the first step is somewhat difficult to visualize, the second can be computationally challenging. In the 1990's, Casson and Rivin independently discovered a method for solving for the complete hyperbolic structure, which involves volume maximization across possible angle structures on the tetrahedra in a given triangulation. In a lovely article written by Guerítaud (with an extended appendix by Futer), they apply the Casson-Rivin program to triangulations of punctured torus bundles (and 2-bridge knots and links). Their starting decompositions, which are examples of Agol's veering triangulations, are constructed in a manner fundamentally different from the decompositions found in Thurston's work. In this talk, you will see explicit examples of both types of decompositions of link complements, as well as preliminary work extending Guerítaud and Futer's approach to hyperbolic closed 3-braids.