Topology & Group Theory Seminar

Vanderbilt University

2018/2019

Links to seminar schedule for previous years:

2010/11,
2011/12,
2012/13,
2014/15,
Spring 2016,
Fall 2016,
Spring 2017,
2017/18,
2018/19

Organizer: Spencer Dowdall

Wednesdays, 4:10–5:00pm in SC 1308 (unless otherwise noted)

** Wednesday, August 28, 2019 **

Kevin Schreve (University of Chicago)

Title: Proper actions versus uniform embeddings

Absract: Whenever a finitely generated group \(G\) acts properly discontinuously by isometries on a metric space \(X\), there is an induced uniform embedding (a Lipschitz and uniformly proper map) \(f \colon G\to X\) given by mapping \(G\) to an orbit. I will talk about some examples of groups which uniformly embed into a contractible n-manifold but do not act on a contractible n-manifold. Kapovich and Kleiner constructed torsion-free hyperbolic groups that embed into \(\mathbb{R}^3\) but only act on \(\mathbb{R}^4\). My main application will be showing that certain k-fold direct products of these groups do not act on \(\mathbb{R}^{3k}\).

Matthew Haulmark (Vanderbilt)

Title: Canonical JSJ for Relatively Hyperbolic Groups

Abstract: JSJ decompositions first appeared in the context of 3-manifolds with the work of Jaco-Shalen and Johannson. Generalizations of JSJ theory to finitely generated groups have been studied in different contexts by many authors (Kropholler, Rips-Sela, Papasoglu-Swenson, Bowditch, Guirardel-Levitt, etc.). Guirardel and Levitt have shown that if G is one ended and hyperbolic relative to a finite collection of finitely generated subgroups, then there is a relative JSJ tree for G over the class of elementary subgroups. In a joint work with Chris Hruska we show that Guirardel and Levitt’s result can be obtained from the topology of the Bowditch boundary. This implies that the relative JSJ tree for G is a “relative” quasi-isometry invariant.

No Seminar

Simon Andre (Vanderbilt)

Title: Hyperbolicity is preserved under elementary equivalence

Abstract: Zlil Sela proved that a finitely generated group that satisfies the same first-order properties as a torsion-free hyperbolic group is torsion-free hyperbolic. I will explain that this result remains true for hyperbolic groups with torsion, as well as for subgroups of hyperbolic groups, and for hyperbolic and cubulable groups.

Rachel Skipper (OSU)

Title: Finiteness Properties for Simple Groups

Abstract: A group is said to be of type $F_n$ if it admits a classifying space with compact \(n\)-skeleton. We will consider the class of Röver-Nekrachevych groups, a class of groups built out of self-similar groups and Higman-Thompson groups, and use them to produce a simple group of type \(F_{n-1}\) but not \(F_n\) for each \(n\). These are the first known examples for \(n\geq 3\). As a consequence, we find the second known infinite family of quasi-isometry classes of finitely presented simple groups.

Jean Pierre Mutanguha (Arkansas)

Title: The irreducibility of monodromy is a mapping torus invariant

Abstract: An immediate corollary of Nielsen-Thurston classification of surface homeomorphisms is that if two surface homeomorphisms f and g have homeomorphic mapping tori, then f is pseudo-Anosov if and only if g is pseudo-Anosov. Using hyperbolization theorem and rigidity results, the hypothesis can be weakened to quasi-isometric mapping tori. We show an analogous result for free group automorphisms: if two free group automorphisms have isomorphic mapping tori, then the first automorphism is fully irreducible and atoroidal if and only if the other is fully irreducible and atoroidal. This answers a question posed by Dowdall-Kapovich-Leininger.

Levi Sledd (Vanderbilt)

Title/Abstract: TBA

Daniel Studenmund (Notre Dame)

Title/Abstract: TBA

Lauren Ruth (Vanderbilt)

Title/Abstract: TBA

Jason Behrstock (CUNY)

Title/Abstract: TBA

No Seminar (Thanksgiving break)

Genevieve Walsh (Tufts)

Title/Abstract: TBA

No Seminar (Spring Break)

Michael Hull (University of North Carolina, Greensboro)

Title/Abstract: TBA

No Seminar (Start of summer holiday)