Neil Strickland (University of Sheffield)
N.P.Strickland@sheffield.ac.uk
There is a well-known connection between formal groups and complex orientable cohomology theories, with the theory of complex cobordism playing a universal role. I will report on work in progress aimed at developing an equivariant version of this connection. The algebrogeometric viewpoint, which is already very useful in the nonequivariant context, becomes almost essential equivariantly. A key point is that the generalised equivariant cohomology of CP\infty is no longer just a formal power series ring in one variable (or equivalently, the ring of functions on a formal curve); but it is still the ring of functions on a "formal multicurve".
As a side product of this work, I will give an explicit presentation of the Z/2 equivariant complex cobordism ring, which was previously only understood in a rather indirect way.