Abstract
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.
Citation
Aravind Asok. Kirsten Wickelgren. Ben Williams. "The simplicial suspension sequence in $\mathbb{A}^1\mskip-2mu$–homotopy." Geom. Topol. 21 (4) 2093 - 2160, 2017. https://doi.org/10.2140/gt.2017.21.2093
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