By Marek Kuś
Equivariant elliptic cohomology
Appears in collection : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs
Inspired by the triad of rational, trigonometric and elliptic functions appearing in representation theory, Grojnowski defined in 1995 a higher analogue of equivariant ordinary cohomology and equivariant K-theory: equivariant elliptic cohomology. However, his approach only works over the complex numbers. Based on ideas of Lurie, David Gepner and I have recently defined equivariant elliptic cohomology without these restrictions. This allows in particular to refine topological modular forms to a genuine equivariant theory.