Topology Seminar
|
Mon, 10/10/2011 15:45 |
Arthur Bartels (Muenster/Oxford) |
Topology Seminar  |
L3 |
| 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, 17/10/2011 15:45 |
Andrew Baker (Glasgow) |
Topology Seminar |
L3 |
| 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, 24/10/2011 15:45 |
Nick Wright (Southampton) |
Topology Seminar |
L3 |
| 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, 31/10/2011 15:45 |
Ilya Kazachkov (Oxford) |
Topology Seminar |
L3 |
|
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, 07/11/2011 15:45 |
Ric Wade (Oxford) |
Topology Seminar |
L3 |
Automorphisms of right-angled Artin groups interpolate between  and  . An active area of current research is to extend properties that hold for both the above groups to  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, 14/11/2011 15:45 |
Henry Wilton |
Topology Seminar |
L3 |
|
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, 21/11/2011 15:45 |
Brendan Owens (Glasgow) |
Topology Seminar |
L3 |
| 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, 28/11/2011 15:45 |
Danny Calegari (Cambridge) |
Topology Seminar |
L3 |
| 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. | |||
