The simplicial suspension sequence in 𝔸1 –homotopy

2015/07/31 by Aravind Asok, Kirsten Wickelgren, Ben Williams
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Exact sequence #Homotopy and Cohomology in Algebraic Topology #Limit of a sequence #Loop (graph theory) #Sequence (biology) #Space (punctuation) #Suspension (topology) #math.AG #math.AT #math.KT #msc:14F42 #msc:19E15 #msc:55Q02

paper · pdf · doi:10.2140/gt.2017.21.2093

published as Geom. Topol. 21 (2017) 2093-2160 · 56 pages; Accepted for publication G&T

openalex created_date 2016/06/24 · arxiv created 2016/08/20 · openalex publication_date 2017/05/19 · arxiv updated 2017/06/14 · openalex updated_date 2026/08/05

Abstract

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

Citations

• Reduced power operations in motivic cohomology
• Motivic cohomology with 𝐙 / 2 -coefficients
• Cohomologie modulo 2 des complexes d’Eilenberg-MacLane
• Algebraic vector bundles on spheres
• On Adding Relations to Homotopy Groups
• Homotopical Algebra
• On the Freudenthal Theorems
• Simplicial Homotopy Theory