J. D. Quigley: New infinite families in the stable homotopy groups of spheres

Abstract.

Computing the stable homotopy groups of spheres is a fundamental problem in algebraic topology. In previous work, Behrens, Mahowald, and I used the Hurewicz homomorphism for topological modular forms, a generalized homology theory, to detect many infinite families of elements in these groups. I will review these results and then discuss recent work with Bhattacharya and Bobkova producing several new infinite families with trivial image under the tmf-Hurewicz homomorphism.