Please mark your calendars for the upcoming Twenty-Eighth Annual Workshop in Geometric Topology. This summer's workshop will be held at Treasure Mountain Inn in Park City, UT on May 23-25. Principal speaker David Gabai will give a series of three one-hour presentations. In addition, participants will have the opportunity to give 20-25 minute talks on their own work.
NSF funds allow us to cover part of the travel expenses for participants without other means of support. Graduate students working in geometric topology and geometric group theory are especially encouraged to apply for funding. If you plan to apply for funding, please contact Eric Swenson before April 4th.
The featured speaker is David Gabai of Princeton.
Title: Three lectures on the topology of ending lamination spaces.
Abstract: Ending laminations play central roles in low dimensional topology, hyperbolic geometry and geometric group theory. For example, stable and unstable laminations of pseudo-Anosov mappings are ending laminations and ending laminations parametrize certain deformation spaces of hyperbolic 3-manifolds. These lectures will address the topology of ending lamination spaces. In particular the theorem that if S is a finite type hyperbolic surface, then EL(S) is (n-1)-connected and (n-1)-locally connected where dim(PML(S))=2n+1. Furthermore, if S is a (p+n)-punctured sphere, then EL(S) is homeomorphic to the n-dimensional Nobeling space. This relies on the recent characterization of Nobeling spaces by Ageev, Levin and Nagorko. The theorem for n=1 is due to S. Hensel and P. Przytycki
Lecture I: Ending laminations and Nobeling spaces will be introduced. The main results and some basic techniques will be presented. Open problems including possible connections with other Nobeling type spaces will be stated.
Lectures II, III: The heart of this work is about how, under the right hypotheses, to approximate a map into EL(S) by a map into PML(S) and how to approximate a map into PML(S) by a map into EL(S). The second and third lectures will focus on these core issues.
Eric Swenson, Brigham Young University (eric@math.byu.edu)
Ric Ancel, UW-Milwaukee
Fred Tinsley, Colorado College
Craig Guilbault, UWisconsin-Milwaukee
Dennis Garity, Oregon State University
Gerard Venema, Calvin College
David Wright, Brigham Young University