# Fifty-first meeting of the Transpennine Topology Triangle

## Department of Pure Mathematics

University of Sheffield

Friday, October 21st 2005

This will be a working meeting. There will therefore be the usual time for
participant discussion.

## Programme

- 11.00 am: Coffee in I15

- 11.30 am, J11: Jeff Giansiracusa

``Mapping class groups of simply-connected 4-manifolds
and characteristic classes''
- 2.00 pm J11: Richard Hepworth

``Kreck-Stolz invariants''
- 3.00 pm, I15: Tea
- 4.00 pm, J11: Marcello Felisatti (Leicester)

TTBA

We expect to go to eat nearby, soon after the
last talk.

### Abstracts

- Mapping class groups of simply-connected 4-manifolds
and characteristic classes

We study the mapping class groups of simply-connected 4-manifolds. By
taking connected sums with CP^2 \# \overline{CP^2} one can define a
stable mapping class group. We show that this stable group is in fact
independent of the initial manifold, and it is isomorphic to the
stabilized group of automorphisms of the intersection form.
As a corollary, the homotopy type of a cobordism category of
simply-connected 4-manifolds is the Hermitian K-theory of the integers.
We then consider the (unstable) cohomology of mapping class groups of
4-manifolds and describe progress towards proving a version of Harer's
stability in dimension 4.

- Kreck-Stolz invariants

In 1988, Kreck & Stolz introduced new invariants of certain
7-manifolds and showed that the invariants completely classify the
manifolds. I will give a generalization of these results and describe how
one can interpret the invariants using K-theory and secondary operations
(and perhaps tmf).

Anyone who wishes to participate is welcome: we shall operate the usual
arrangements for assistance with travel expenses. We expect to assemble for tea
and coffee in I15, Floor 5, from 11.00 am until the first talk. Each lecture
will take place in Room J11 of the Hicks Building, Hounsfield Road,
Sheffield.

Tea and Coffee will be served in the common room I15.

For
further information email John Greenlees j.greenlees@sheffield.ac.uk, (or
John Hunton jrh7@mcs.le.ac.uk or Nige Ray
nige@ma.man.ac.uk) if you are interested,
so we can make approximately the right amount of tea and coffee.

## How to get there

From the rail station, you can catch the Number 60 bus,
and get off where it crosses the ring road. Or take the supertram to the
University stop. There is more information at
School of Mathematics and Statistics
Homepage

The meeting is partially supported by a Scheme 3 grant from the London
Mathematical Society.

## Escape routes

Back to TTT Homepage

To TTT50

To TTT52