# TTT110: Liverpool

University of Liverpool.

Supported by the London Mathematical Society.

## Date

15 May 2019

## Speakers

### Ian Leary (Southampton)

Bestvina-Brady groups, generalisations and applications

Bestvina-Brady groups, generalisations and applications

Abstract: In the 1990s, Bestvina-Brady solved a long-standing problem by constructing the first examples of groups that are 'almost finitely presented' but not finitely presented. I'll describe their construction, my recent generalisation of it, and an application related to the Higman embedding theorem.

### Toby Hall (Liverpool)

Inverse limits of tent maps and sphere homeomorphisms

Inverse limits of tent maps and sphere homeomorphisms

Abstract: The inverse limit construction allows the study of a dynamical system – a self-map of a topological space – to be converted into the study of a self-homeomorphism of the inverse limit. The inverse limit is usually much more complicated than the original space: for example, inverse limits of tent maps – simple piecewise affine self-maps of an interval – typically contain indecomposable continua.

In this talk I'll describe how mild identifications on the inverse limits of tent maps turn them into 2-spheres, and make it possible to construct a parameterised family of sphere homeomorphisms corresponding to the parameterized family of tent maps. I'll discuss the dynamics of these homeomorphisms, which include examples of Thurston's pseudo-Anosov maps, so-called generalised pseudo-Anosovs, and the (further generalised) measurable pseudo-Anosovs.

The talk will start with an extended introduction to relevant ideas in dynamical systems theory, aimed at non-specialists. This is joint work with Philip Boyland (University of Florida) and Andre' de Carvalho (University of Sao Paulo).

### Ieke Moerdijk (Utrecht / Sheffield)

Dendroidal spaces and mapping spaces between little cubes operads

Dendroidal spaces and mapping spaces between little cubes operads