# TTT84: Sheffield

The University of Sheffield.

Supported by the London Mathematical Society.

## Date

11 July 2012

## Speakers

### Philipp Wruck (Sheffield)

Uniqueness of equivariant Lefschetz numbers and some consequences

Uniqueness of equivariant Lefschetz numbers and some consequences

There are several notions of equivariant Lefschetz numbers in the literature. The main differences arise from basic properties of the action and the acting group, and whether one wants the Lefschetz number to be localized around fixed points or rather fixed orbits.

I will discuss several approaches and give a sketch of proof that, after fixing some simple data via axioms, an equivariant Lefschetz number is unique. In the second part, I will give an outlook on topological equivariant intersection theory and how this can be used to give yet another description of a Lefschetz invariant which hopefully may be used for generalisations, eg to flows.

### Peter Eccles (Manchester)

Self-intersection manifolds of immersions

Self-intersection manifolds of immersions

Given a self-transverse immersion of a closed smooth manifold M of dimension n-k in a smooth manifold N of dimension n, the r-fold self-intersection set is the image of a closed manifold of dimension n-rk. A natural question is to ask which bordism classes of manifolds of dimension n-rk arise in this way for given N.

I will describe a general approach to this problem, illustrate it with some examples indicating in particular how it relates to some classical invariants in homotopy theory such as the Hopf invariant and Kervaire invariant.

### Andy Baker (Glasgow)

Calculations with commutative S-algebras

Calculations with commutative S-algebras

Commutative S-algebras are a modern incarnation of E-infinity ring spectra. I'll discuss some constructions and show how to do calculations with some examples using topological Andre-Quillen theory. I'll give the background necessary to follow this.