Past Seminars › Seminar Series

Topology Seminar (past)

Mon, 06/02/2012
13:00 		Ruth Charney (Brandeis) Topology Seminar Add to calendar L3
Length functions of right-angled Artin groups
Morgan and Culler proved in the 1980’s that a minimal action of a free group on a tree is completely determined by its length function. This theorem has been of fundamental importance in the study of automorphisms of free groups. In particular, it gives rise to a compactification of Culler-Vogtmann's Outer Space. We prove a 2-dimensional analogue of this theorem for right-angled Artin groups acting on CAT(0) rectangle complexes. (Joint work with M. Margolis)
Mon, 06/02/2012
03:45 		Ian Leary (Southampton) Topology Seminar Add to calendar L3
Variations on a theme of Eilenberg-Ganea

The Eilenberg-Ganea conjecture is the statement that every group of cohomological dimension two admits a two-dimensional classifying space.  This problem is unsolved after 50 years.  I shall discuss the background to this question and negative answers to some other related questions.  This includes recent joint work with Martin Fluch.
Mon, 30/01/2012
15:45 		Chris Cashen Topology Seminar Add to calendar L3
Line Patterns in Free Groups
I will discuss quasi-isometries of the free group that preserve an equivariant pattern of lines. There is a type of boundary at infinity whose topology determines how flexible such a line pattern is. For sufficiently complicated patterns I use this boundary to define a new metric on the free group with the property that the only pattern preserving quasi-isometries are actually isometries.
Mon, 23/01/2012
15:45 		Gerald Besson Topology Seminar Add to calendar L3
Differentiable rigidity and Ricci curvature
Mon, 16/01/2012
15:45 		Richard Hepworth (Aberdeen) Topology Seminar Add to calendar L3
String topology of classifying spaces

Chataur and Menichi showed that the homology of the free loop space of the classifying space of a compact Lie group admits a rich algebraic structure: It is part of a homological field theory, and so admits operations parametrised by the homology of mapping class groups.  I will present a new construction of this field theory that improves on the original in several ways: It enlarges the family of admissible Lie groups.  It extends the field theory to an open-closed one.  And most importantly, it allows for the construction of co-units in the theory.  This is joint work with Anssi Lahtinen.
Mon, 28/11/2011
15:45 		Danny Calegari (Cambridge) Topology Seminar Add to calendar L3
Ziggurats and rotation numbers
I will discuss new rigidity and rationality phenomena (related to the phenomenon of Arnold tongues) in the theory of nonabelian group actions on the circle. I will introduce tools that can translate questions about the existence of actions with prescribed dynamics, into finite combinatorial questions that can be answered effectively. There are connections with the theory of Diophantine approximation, and with the bounded cohomology of free groups. A special case of this theory gives a very short new proof of Naimi’s theorem (i.e. the conjecture of Jankins-Neumann) which was the last step in the classification of taut foliations of Seifert fibered spaces. This is joint work with Alden Walker.
Mon, 21/11/2011
15:45 		Brendan Owens (Glasgow) Topology Seminar Add to calendar L3
Concordance groups of links
The concordance group of classical knots C was introduced over 50 years ago by Fox and Milnor. It is a much-studied and elusive object which among other things has been a valuable testing ground for various new topological (and smooth 4-dimensional) invariants. In this talk I will address the problem of embedding C in a larger group corresponding to the inclusion of knots in links.
Mon, 14/11/2011
15:45 		Henry Wilton Topology Seminar Add to calendar L3
One-ended subgroups of graphs of free groups

A longstanding question in geometric group theory is the following. Suppose G is a hyperbolic group where all finitely generated subgroups of infinite index are free. Is G the fundamental group of a surface? This question is still open for some otherwise well understood classes of groups. In this talk, I will explain why the answer is affirmative for graphs of free groups with cyclic edge groups. I will also discuss the extent to which these techniques help with the harder problem of finding surface subgroups.
Mon, 07/11/2011
15:45 		Ric Wade (Oxford) Topology Seminar Add to calendar L3
Right-angled Artin groups and their automorphisms
Automorphisms of right-angled Artin groups interpolate between $ Out(F_n) $ and $ GL_n(\mathbb{Z}) $. An active area of current research is to extend properties that hold for both the above groups to $ Out(A_\Gamma) $ for a general RAAG. After a short survey on the state of the art, we will describe our recent contribution to this program: a study of how higher-rank lattices can act on RAAGs that builds on the work of Margulis in the free abelian case, and of Bridson and the author in the free group case.
Mon, 31/10/2011
15:45 		Ilya Kazachkov (Oxford) Topology Seminar Add to calendar L3
Group actions on real cubings

We introduce the notion of a real cubing. Roughly speaking, real cubings are to CAT(0) cube complexes what real trees are to simplicial trees. We develop an analogue of the Rips’ machine and establish the structure of groups acting nicely on real cubings.
Mon, 24/10/2011
15:45 		Nick Wright (Southampton) Topology Seminar Add to calendar L3
Asymptotic dimension for CAT(0) cube complexes
In this talk I'll explain how to build CAT(0) cube complexes and construct Lipschitz maps between them. The existence of suitable Lipschitz maps is used to prove that the asymptotic dimension of a CAT(0) cube complex is no more than its dimension.
Mon, 17/10/2011
15:45 		Andrew Baker (Glasgow) Topology Seminar Add to calendar L3
BP: Close encounters of the E-infinity kind
The notion of an E-infinity ring spectrum arose about thirty years ago, and was studied in depth by Peter May et al, then later reinterpreted in the framework of EKMM as equivalent to that of a commutative S-algebra. A great deal of work on the existence of E-infinity structures using various obstruction theories has led to a considerable enlargement of the body of known examples. Despite this, there are some gaps in our knowledge. The question that is a major motivation for this talk is `Does the Brown-Peterson spectrum BP for a prime p admit an E-infinity ring structure?'. This has been an important outstanding problem for almost four decades, despite various attempts to answer it. I will explain what BP is and give a brief history of the above problem. Then I will discuss a construction that gives a new E-infinity ring spectrum which agrees with BP if the latter has an E-infinity structure. However, I do not know how to prove this without assuming such a structure!
Mon, 10/10/2011
15:45 		Arthur Bartels (Muenster/Oxford) Topology Seminar Add to calendar L3
Invitation to the Farrell-Jones Conjecture
The Farrell-Jones Conjecture predicts a homological formula for K-and L-theory of group rings. Through surgery theory it is important for the classification of manifolds and in particular the Borel conjecture. In this talk I will give an introduction to this conjecture and give an overview about positive results and open questions.
Mon, 27/06/2011
15:45 		Alexander Olshanskii (Vanderbilt) Topology Seminar Add to calendar L3
Length and degree distortion in groups and algebras
Distortion is an asymptotic invariant of the embeddings of finitely generated algebras. For group embeddings, it has been introduced by M.Gromov. The main part of the talk will be based on a recent work with Yu.Bahturin, where we consider the behavior of distortion functions for subalgebras of associative and Lie algebras.
Mon, 20/06/2011
15:45 		Voughan Jones (Berkeley) Topology Seminar Add to calendar L3
The classification of subfactors of small index and the onset of wilderness
In the 1990's Haagerup discovered a new subfactor, and hence a new topological quantum field theory, that has so far proved inaccessible by the methods of quantum groups and conformal field theory. It was the subfactor of smallest index beyond 4. This led to a classification project-classify all subfactors to as large an index as possible. So far we have gone as far as index 5. It is known that at index 6 wildness phenomena occur which preclude a simple listing of all subfactors of that index. It is possible that wildness occurs at a smaller index value, the main candidate being approximately 5.236.
Mon, 06/06/2011
15:45 		John Francis (Northwestern) Topology Seminar Add to calendar L3
E_n-rings and factorization homology
Mon, 30/05/2011
15:45 		Goulnara Arzhantseva (Vienna) Topology Seminar Add to calendar L3
Coarse non-amenability and coarse embeddings
Mon, 23/05/2011
15:45 		Remi Coulon (MPI Bonn) Topology Seminar Add to calendar L3
Examples of aspherical hyperbolic simplicial complexes. An application of small cancellation for rotation families of groups
The goal of this talk is to construct new examples of hyperbolic aspherical complexes. More precisely, given an aspherical simplicial complex P and a subcomplex Q of P, we are looking for conditions under which the complex obtained by attaching a cone of base Q on P remains aspherical. If Q is a set of loops of a 2-dimensional complex, J.H.C. Whitehead proved that this new complex is aspherical if and only if the elements of the fundamental group of P represented by Q do not satisfy any identity. To deal with higher dimensional subcomplexes we use small cancellation theory and extend the geometric point of view developed by T. Delzant and M. Gromov to rotation families of groups. In particular we obtain hyperbolic aspherical complexes obtained by attaching a cone over the "real part" of a hyperbolic complex manifold.
Mon, 16/05/2011
15:45 		Jessica Banks (Oxford) Topology Seminar Add to calendar L3
The Kakimizu complex of a link
We give an introduction to the Kakimizu complex of a link, covering a number of recent results. In particular we will see that the Kakimizu complex of a knot may be locally infinite, that the Alexander polynomial of an alternating link carries information about its Seifert surfaces, and that the Kakimizu complex of a special alternating link is understood.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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