The simplicial suspension sequence in A1 -homotopy


Journal Article

© 2017, Mathematical Sciences Publishers. All rights reserved. We study a version of the James model for the loop space of a suspension in unstable A1-homotopy theory. We use this model to establish an analog of G W Whitehead’s classical refinement of the Freudenthal suspension theorem in A1-homotopy theory: our result refines F Morel’s A1-simplicial suspension theorem. We then describe some E1-differentials in the EHP sequence in A1-homotopy theory. These results are analogous to classical results of G W Whitehead. Using these tools, we deduce some new results about unstable A1-homotopy sheaves of motivic spheres, including the counterpart of a classical rational nonvanishing result.

Full Text

Duke Authors

Cited Authors

  • Asok, A; Wickelgren, K; Williams, B

Published Date

  • May 19, 2017

Published In

Volume / Issue

  • 21 / 4

Start / End Page

  • 2093 - 2160

Electronic International Standard Serial Number (EISSN)

  • 1364-0380

International Standard Serial Number (ISSN)

  • 1465-3060

Digital Object Identifier (DOI)

  • 10.2140/gt.2017.21.2093

Citation Source

  • Scopus