BooksStandalone TitlesCollected Volumepp. 2768–2790

Stable homotopy groups of spheres and motivic homotopy theory

  • Daniel C. Isaksen

    Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

  • Guozhen Wang

    Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, China

  • Zhouli Xu

    Department of Mathematics, University of California San Diego, La Jolla, CA 92093, USA
Stable homotopy groups of spheres and motivic homotopy theory cover
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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.