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The simplicial suspension sequence in A^1-homotopy
- Source :
- Geom. Topol. 21 (2017) 2093-2160
- Publication Year :
- 2015
-
Abstract
- We study a version of the James model for the loop space of a suspension in unstable ${\mathbb A}^1$-homotopy theory. We use this model to establish an analog of G.W. Whitehead's classical refinement of the Freudenthal suspension theorem in ${\mathbb A}^1$-homotopy theory: our result refines F. Morel's ${\mathbb A}^1$-simplicial suspension theorem. We then describe some $E_1$-differentials in the EHP sequence in ${\mathbb A}^1$-homotopy theory. These results are analogous to classical results of G.W. Whitehead's. Using these tools, we deduce some new results about unstable ${\mathbb A}^1$-homotopy sheaves of motivic spheres, including the counterpart of a classical rational non-vanishing result.<br />Comment: 56 pages; Accepted for publication G&T
Details
- Database :
- arXiv
- Journal :
- Geom. Topol. 21 (2017) 2093-2160
- Publication Type :
- Report
- Accession number :
- edsarx.1507.05152
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2140/gt.2017.21.2093