# TTT54: Sheffield

Department of Pure Mathematics, the University of Sheffield.

This was a working meeting with the usual time for participant discussion.

## Date

24 April 2006

## Speakers

Catherina Stroppel (Glasgow)

Invariants of tangles and cobordisms via representation theory

Vitaliy Kurlin (Liverpool)

Compressed Campbell-Baker-Hausdorff formula with applications to complex cobordism

Nige Ray (Manchester)

2- and 3-spheres in equivariant complex cobordism

## Abstracts

### Compressed Campbell-Baker-Hausdorff formula with applications to complex cobordism

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.

## Further information

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