The 32nd Annual
Workshop in
Geometric Topology
Texas Christian University
Fort Worth, Texas
June 25 - 27, 2015
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The 32nd Annual
Workshop in
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The featured speaker is Wolfgang Lück of the University of Bonn and the Hausdorff Research Institute for Mathematics, who will give a series of three one-hour lectures. Titles and abstracts can be found below.
Participants are invited to contribute talks of 20 to 30 minutes. Abstracts may be entered on the registration form or sent directly to Greg Friedman (send email).
Financial support is available to help defer the travel and living expenses of participants who do not have other funding for their research. Such support can be requested on the registration form. Requests for support must be received by May 11. Graduate students and recent PhDs in geometric topology are especially encouraged to apply.
The workshop will be supported by a grant from the National Science Foundation (DMS-1461385), by the TCU College of Science and Engineering, and by the TCU Department of Mathematics.
To defray local costs, a $25 registration fee will be collected on site.
Introduction to L2-invariants: We give an introduction to L2-homology and L2-Betti numbers which generalizes the well-known classical notions of homology and Betti numbers. They have suprising applications to problems in topology, geometry, and group theory which a priori seem not to be related but whose proofs require L2-techniques. We also discuss some open conjectures and will briefly treat L2-torsion, which is the analogue of Reidemeister torsion.
Introduction to the Farrell-Jones Conjecture: The Farrell-Jones Conjecture identifies the algebraic K- and L-groups for group rings to certain equivariant homology groups. We will not focus on the technical details of the precise formulation or of the proofs but try to convince the audience about its significance by considering special cases and presenting the surprizing large range of its applications to prominent problems in topology, geometry, and group theory. This talk will be independent of the the first talk.
Some applications to 3-manifolds: Thanks to the recent breakthrough about the Fibering Conjecture due to Agol and others, there are nice applications of L2-invariants to 3-manifolds which also use the Farrell-Jones Conjecture. Essentially we will introduce and relate four invariants which are of different natures: the Thurston norm, the degree of higher order Alexander polynomials, the degree of the L2-torsion function, and a version of the L2-Euler characteristic. We will use some of the results of the first two talks here, but this talk will nevertheless be self-contained.
Fredric Ancel, University of Wisconsin-Milwaukee
Greg Friedman, Texas Christian University
Craig Guilbault, University of Wisconsin-Milwaukee
Eric Swenson, Brigham Young University
Frederick Tinsley, Colorado College
Gerard Venema, Calvin College
Contact Greg Friedman (send email) if you have questions about the workshop or comments on this web site.