**Papers Published**

- Asok, A; Wickelgren, K; Williams, B,
*The simplicial suspension sequence in A*, Geometry & Topology, vol. 21 no. 4 (May, 2017), pp. 2093-2160^{1}-homotopy

(last updated on 2022/08/07)**Abstract:**

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 Whiteheadâ€™s classical refinement of the Freudenthal suspension theorem in A1-homotopy theory: our result refines F Morelâ€™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.