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The
simplicial suspension sequence in
$\mathbb{A}^1\mskip-2mu$–homotopy
Aravind Asok, Kirsten Wickelgren and Ben Williams |
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Geometry & Topology 21 (2017) 2093–2160
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Abstract |
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We study a version of the James model for the loop space of a suspension in unstable –homotopy theory. We use this model to establish an analog of G W Whitehead’s classical refinement of the Freudenthal suspension theorem in –homotopy theory: our result refines F Morel’s –simplicial suspension theorem. We then describe some –differentials in the EHP sequence in –homotopy theory. These results are analogous to classical results of G W Whitehead. Using these tools, we deduce some new results about unstable –homotopy sheaves of motivic spheres, including the counterpart of a classical rational nonvanishing result. |
Keywords
$A^1$-homotopy, James construction
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Mathematical Subject Classification 2010
Primary: 14F42, 19E15
Secondary: 55Q15, 55Q20, 55Q25
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References |
Publication
Received: 6 August 2015
Revised: 7 July 2016
Accepted: 18 August 2016
Published: 19 May 2017
Proposed: Haynes Miller
Seconded: Peter Teichner, Mark Behrens
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Authors |
| Aravind Asok | |
| Department of Mathematics University of Southern California 3620 S Vermont Ave Los Angeles, CA 90089-2532 United States |
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| Kirsten Wickelgren | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30308 United States |
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| Ben Williams | |
| Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver BC V6T 1Z2 Canada |
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