# Fifty-second Meeting of the Transpennine Topology Triangle

## School of Mathematics

University of Manchester

Tuesday 6
December 2005

## Programme

The talks will take place in the Mathematics and Social
Science Building, at the north-east corner of the campus. This building is
number 21 on the University Campus
map, and lies within 5 minutes walk of Piccadilly railway station.
Participants will meet for coffee from 1100AM onwards in the Staff Common Room
N2. Lunch will be taken in any of several local venues (such as the vegetarian
"On the Eight Day", for example), and we expect to visit a nearby restaurant for
early-evening dinner.
- 11.00-11.30: COFFEE (Room N2)

- 11.30-12.20, Room B009: Andrew Baker (Glasgow)

GAMMA-COHOMOLOGY OF RINGS
OF NUMERICAL POLYNOMIALS, AND E-INFINITY STRUCTURES ON K-THEORY

There is an obstruction theory for E-infinity structures on commutative
ring spectra which makes use of Gamma-cohomology, defined by Robinson and
Whitehouse. This is a cohomology theory for commutative rings that is closely
related to Andre-Quillen cohomology as well as to the obstruction theory of
Goerss and Hopkins.

- 12.30-2.00: LUNCH

- 2.00-2.55, Room B010: Francis Clarke (Swansea)

ENUMERATING ABELIAN
GROUPS

How many finite abelian groups are there? More precisely, given a finite
set, how many of the binary operations on it make it into an abelian group? A
recursion for this function is a key component in Cohen-Lenstra heuristics on
the distribution of class groups. I shall give a bijective proof of the
recursion in which the essential ingredient is a piece of labelled homological
algebra.

- 3.00-3.45: TEA (Room N2)

- 3.45-4.35, Room B010: Andrey Lazarev (Bristol)

TBA

Everyone who wishes to participate is welcome, particularly postgraduate
students. We shall operate the usual criterea for assistance with travel
expenses, but beneficiaries will need to complete the standard UM green form.
Those who qualify should therefore come armed with their NI numbers, and details
of their UK bank accounts. Please email MIMS secretary Louise Stait if you are interested in
attending, so that we can cater for appropriate numbers.

The meeting is jointly supported by the London Mathematical Society and
MIMS.

## Escape routes

TTT Homepage

TTT51

TTT53

Manchester School of Mathematics