# Fifty-fourth meeting of the Transpennine Topology Triangle

## Department of Pure Mathematics

University of Sheffield

Monday, 24th April 2006

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, Northcott Room J11: Catherina Stroppel (Glasgow)

``Invariants of tangles and cobordisms via representation theory.''
- 2.00 pm, Northcott Room J11: Vitaliy Kurlin (Liverpool)

Compressed Campbell-Baker-Hausdorff formula with applications to
complex cobordism.
- 3.00 pm, I15: Tea
- 4.00 pm, Northcott Room J11: Nige Ray (Manchester)

``2- and 3-spheres in equivariant complex cobordism''

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

### Abstracts

Vitaliy Kurlin:

Classical Baker-Campbell Hausdorff formula gives a recursive way to compute
Z=log(exp(X)exp(Y)) via commutators of X and Y. The series Z lives in the free
Lie algebra L generated by X and Y. The first aim of the talk is to present a
closed compressed version of Baker-Campbell-Hausdorff formula in the quotient
L/[[L,L],[L,L]]. This result turned out to be a powerful tool for solving
exponential equations in Lie algebras. The compressed formula allowed us to solve
completely complicated equations defining compressed Drinfeld associators and
involving 5 and 6 exponentials. The second aim is to apply the compressed formula
to the Lie algebra of formal vector fields on the real line. The enveloping algebra
of the above Lie algebra is isomorphic to the Landveber-Novikov algebra of
cohomological operations in cobordisms.

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

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