# TTT89: Leicester

University of Leicester.

Supported by the London Mathematical Society.

## Date

22 November 2013

## Speakers

### Alex Clark (Leicester)

Homotopy pro-groups in the classification of minimal sets of foliations

Homotopy pro-groups in the classification of minimal sets of foliations

Abstract: We will examine a natural class of minimal sets of foliations and the settings in which they arise. We will give a dynamical and topological characterisation of these minimal sets and examine how they can be usefully analysed with the aid of homotopy pro-groups. This leads to a topological classification of these minimal sets in certain cases. These considerations lead to a generalised Borel conjecture for those members of this class of spaces which are aspherical in a sense we will make precise.

### Markus Szymik (Copenhagen)

Homotopy coherent centres

Homotopy coherent centres

Abstract: In this talk, I will first motivate and define a homotopy coherent refinement of the usual notion of a centre of a category in contexts with an associated homotopy theory. Then, after presenting some basic properties, I will focus on calculations and examples, most of them based on joint work with W G Dwyer or E Meir.

### Dorette Pronk (Dalhousie)

Orbi Mapping Spaces

Orbi Mapping Spaces

Abstract: I will discuss the orbispace structure on a mapping space of orbispaces in terms of proper etale groupoids. It is relatively easy to give the mapping groupoid that represents the groupoid homomorphisms between two topological groupoids. But the situation for orbispaces is more complicated, because we work with generalised maps between groupoids and such maps are given by spans where the left-hand arrow is an essential equivalence.

I will construct the groupoid that represents the mapping orbispace both from first principles and as a pseudo colimit of a diagram of groupoid mapping spaces. In the process I will show that the hom-categories in a bicategory of fractions can be viewed as pseudo colimits of certain categories of fractions.

I will also present some concrete examples and show how the inertia orbifold of an orbifold can be viewed as a mapping space into that orbifold. This is joint work with Vesta Coufal, Carmen Rovi, Laura Scull and Courtney Thatcher.