Topology & Group Theory Seminar
Vanderbilt University

Fall 2009

Organizers: Bruce Hughes and Mark Sapir

Wednesdays, 4:10pm in SC 1310 (unless otherwise noted)

Wednesday, 9 September 2009

Speaker: Stacy Hoehn, Vanderbilt University

Title: The Moduli Space of Compact Topological Fiber Bundle Structures on a Fibration

Abstract: Several classical geometric invariants have parametrized versions that can be used to answer questions about families of spaces.  For example, there is a parametrized version of Wall's finiteness obstruction which can be used to determine when a compact fiber bundle structure can be placed on a fibration whose fibers are finitely dominated.  We will explain how ideas related to this parametrized finiteness obstruction can also be used to compute the moduli space of all such bundle structures on a fibration.




Friday, 18 September 2009

(Joint seminar with the Subfactor Seminar, 4:10 pm in SC 1432)

Speaker: Michael V. Ershov, University of Virginia

Title: Kazhdan quotients of Golod-Shafarevich groups

Abstract: Informally speaking, a finitely generated group G is said to be Golod-Shafarevich (with respect to a prime p) if it has a presentation

with a small set of relators, where relators are counted with different weights depending on how deep they lie in the Zassenhaus p-filtration. Golod-Shafarevich groups are known to behave like (non-abelian) free groups in many ways: for instance, every

Golod-Shafarevich group G has an infinite torsion quotient, and the pro-p completion of G contains a non-abelian free pro-p group.

In this talk I will extend the list of known largeness properties of Golod-Shafarevich groups by showing that they always have an infinite quotient with Kazhdan's property (T). An important consequence of this result is a positive answer to a well-known question on non-amenability of Golod-Shafarevich groups.



Wednesday, 23 September 2009

Speaker: Dongping Zhuang, Vanderbilt University

Title: Introduction to Quasimorphisms 
Abstract: I'll introduce the concept of quasimorphism and discuss its applications in geometric group theory.



Wednesday, 30 September 2009

Speaker: Mike Chance, Vanderbilt University

Title: Degenerate Maxima of Hamiltonian Loops
Abstract: We will discuss topological results of manifolds 
admitting Hamiltonian circle actions as well as those admitting 
certain Hamiltonian loops. We will also discuss the Hofer 
geometry associated to certain symplectic 4-manifolds.




Wednesday, 7 October 2009

Speaker: Alex Furman, University of Illinois at Chicago

Title: Actions of Product Groups on Manifolds

Abstract: This is a joint work with Nicolas Monod. We analyze volume-preserving actions of products of Kazhdan groups on Riemannian manifolds.

Under a natural irreducibility assumption we obtain lower bounds on the dimension of the manifold in terms of the number of factors in the acting group, and strong restrictions for actions of non-linear groups.

We prove our results by means of a new cocycle superrigidity theorem of independent interest, in analogy to Zimmer's programme.



Wednesday, 14 October 2009

Speaker: Wolfgang Steimle, University of Muenster (Germany)

Title: Obstruction to fibering a manifold

Abstract: Given a map f : M --> B between closed topological manifolds, is it homotopic to the projection map of a fiber bundle whose fibers are closed manifolds? If the target space is the circle, and the dimension of M is greater than five, classical results by Farrell show that there are obstructions in algebraic K-theory that vanish if and only if f fibers. The goal of this talk is to show how obstructions to fibering can be defined for arbitrary target spaces B and to indicate why these obstructions reduce to the classical ones in the case B=S^1. This is joint work with F.T. Farrell and Wolfgang Lueck.




Wednesday, 21 October 2009

No seminar



Wednesday, 28 October 2009

Speaker: Ioana Suvaina, Vanderbilt University

Title: Einstein metrics and exotic smooth structures on 4-manifolds



Wednesday, 4 November 2009

Speaker: John Ratcliffe, Vanderbilt University

Title: JSJ Decompositions of Coxeter Groups over FA subgroups

Abstract: A group G has property FA if G fixes a point of every tree on which G acts without inversions.  A Coxeter group W, with finitely many Coxeter generators S, has property FA if and only if the product of any two elements of S has finite order in W.  A visual subgroup of a Coxeter system (W,S) is a subgroup of W generated by a subset of S.  A graph of groups decomposition of a Coxeter system (W,S) is said to be visual if every vertex and edge group is visual.  We prove that every Coxeter system of finite rank has a visual JSJ graph of groups decomposition with edge groups having property FA.  As an application, we reduce the twist conjecture to Coxeter systems that are indecomposable with respect to amalgamated products over visual subgroups with property FA. 


Wednesday, 11 November 2009

Speaker: Mark Sapir, Vanderbilt University

Title: Non-linear matrix groups

Abstract: Joint with Martin Kassabov. We prove that the group EL_n(R) is not linear for many rings R (including the free ring) and n>2.




Wednesday, 18 November 2009

Speaker: Dan Ramras, New Mexico State University

Title: Chern-Weil theory, representation theory, and topological K-theory

Abstract: In a number of computations, it has been observed that below the (rational) cohomological dimension of a group G, there is a discrepancy between the representation theory of G, which is captured by the spaces Hom(G, U(n)), and the topological K-theory of the classifying space of G. This discrepancy is closely analogous to Beilinson-Quillen-Lichtenbaum conjectures relating algebraic K-theory and Galois cohomology. Focusing on the case in which G is the fundamental group of an aspherical, closed manifold, I'll describe joint work with Tom Baird, which explains this phenomenon. The main ingredients are Chern-Weil theory and the homotopical relationship between flat connections, representations, and K-theory. I'll discuss how these results fit with particular examples, including products of surfaces and certain crystallographic groups.



Wednesday, 16 December 2009

Speaker: Romain Tessera, CNRS
Title: A finitely-generated amenable group with very poor compression into Lebesgue spaces


Abstract: We shall discuss the paper by Tim Austin with the above title.