Stable homotopy groups of spheres and motivic homotopy theory
Daniel C. Isaksen
Department of Mathematics, Wayne State University, Detroit, MI 48202, USAGuozhen Wang
Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, ChinaZhouli Xu
Department of Mathematics, University of California San Diego, La Jolla, CA 92093, USA
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Abstract
We consider the problem of computing the stable homotopy groups of spheres, including applications and history. We describe a new technique that yields streamlined computations through dimension 61 and gives new computations through dimension 90 with very few exceptions. We discuss questions and conjectures for further study, including a new approach to the computation of motivic stable homotopy groups over arbitrary base fields. We provide complete charts for the Adams spectral sequence through dimension 90.