Speaker: William Balderrama

Affilliation: University of Virginia

Title: The equivariant J-homomorphism and RO(G)-graded periodic phenomena

Abstract: For a G-representation V, the representation sphere S^V is defined as one-point compactification of V. The G-equivariant stable stems are comprised of equivariant homotopy classes of maps between representation spheres, suitably stabilized. When G is the trivial group, these are the classical stable stems, and a significant amount of work has gone into their computation and into finding regular patterns within them. The first example of such a pattern comes from the J-homomorphism, which produces infinite "v_1-periodic" families in the stable stems.

Early work of Bredon, built on by Landweber, Araki and Iriye, and more recently by Behrens and Shah, has highlighted the existence of certain periodic behavior in C_2-equivariant homotopy theory, not seen nonequivariantly. In this talk, I will describe how a version of the equivariant J-homomorphism can be used to construct these equivariant periodicities, in a way that works in G-equivariant homotopy theory for an arbitrary finite (and to an extent compact Lie) group G.