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The structure of motivic homotopy groups

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Abstract

We study the stable motivic homotopy groups \(\pi _{s,w}\) of the 2-completion of the motivic sphere spectrum over \(\mathbb {C}\). When arranged in the (s, w)-plane, these groups break into four different regions: a vanishing region, an \(\eta \)-local region that is entirely known, a \(\tau \)-local region that is identical to classical stable homotopy groups, and a region that is not well-understood.

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Authors and Affiliations

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

    Bogdan Gheorghe & Daniel C. Isaksen

Authors
  1. Bogdan Gheorghe
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  2. Daniel C. Isaksen
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Correspondence to Bogdan Gheorghe.

Additional information

D. C. Isaksen was supported by NSF Grant DMS-1202213.

We are grateful for the contributions of Sam Gitler, especially for his work on the homotopy types of stunted projective spaces, and for his work on embeddings of projective spaces.

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Gheorghe, B., Isaksen, D.C. The structure of motivic homotopy groups. Bol. Soc. Mat. Mex. 23, 389–397 (2017). https://doi.org/10.1007/s40590-016-0094-x

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