TGTS Tetrahedral Geometry/Topology Seminar

Sponsored by Elizabethtown College, Franklin and Marshall College,
Lebanon Valley College, and Millersville University

Speakers 2014-2015

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 University
TGTS meets at 4:30 p.m. on the first Friday of each month. The public is cordially invited to attend.

Next Talk

    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.

Past Seminars

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