Algebra/Topology seminar

Speaker: Tommaso Rossi

Title: S^1-equivariant homology of the (unordered) configuration spaces of points in the plane

Abstract: In the early nineties Getzler discovered a nice algebraic structure on the equivariant homology of a topological conformal field theory. He called this algebraic structure a "gravity algebra" and he showed that it is governed by an operad which is closely related to H_*(F_n(R^2)/S^1)), where F_n(R^2) is the ordered configuration space of points in the plane. In this talk we will first give an introduction to gravity algebras, providing many interesting examples: the most important will be the S^1-equivariant homology of the free loop space on a manifold. Then I will briefly explain that any class in the S^1-equivariant homology of the (unordered) configuration spaces of points in the plane H_*^{S^1}(C_n(R^2);F_p) (with coefficients in a field F_p of p elements) gives rise to an homology operation for gravity algebras. After that we will see how to compute this equivariant homology and if time permits we will see some applications.