The simplicial suspension sequence in \(\mathbb A^1\)-homotopy

DOI10.2140/gt.2017.21.2093zbMath1365.14027arXiv1507.05152OpenAlexW3121198824MaRDI QIDQ2356961

Ben Williams, Kirsten Wickelgren, Aravind Asok

Publication date: 7 June 2017

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.05152

zbMATH Keywords

\(\mathbb A^1\)-homotopyJames construction

Mathematics Subject Classification ID

Motivic cohomology; motivic homotopy theory (14F42) Algebraic cycles and motivic cohomology ((K)-theoretic aspects) (19E15) Hopf invariants (55Q25) Whitehead products and generalizations (55Q15) Homotopy groups of wedges, joins, and simple spaces (55Q20)

Related Items (11)

Euler class groups and motivic stable cohomotopy (with an appendix by Mrinal Kanti Das) ⋮ An overview of motivic homotopy theory ⋮ Localization and nilpotent spaces in -homotopy theory ⋮ Endomorphisms of the projective plane and the image of the Suslin-Hurewicz map ⋮ Vector bundles on algebraic varieties ⋮ Motivic stable cohomotopy and unimodular rows ⋮ The first stable homotopy groups of motivic spheres ⋮ Generically split octonion algebras and \(\mathbb{A}^1\)-homotopy theory ⋮ On the James and Hilton-Milnor splittings, and the metastable EHP sequence ⋮ Motivic spheres and the image of the Suslin-Hurewicz map ⋮ The simplicial EHP sequence in \(\mathbb{A}^1\)-algebraic topology

Cites Work

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• Algebraic \(K\)-theory and motivic cohomology. Abstracts from the workshop held June 23--29, 2013.
• Stable motivic \(\pi_1\) of low-dimensional fields
• \(\mathbb A^1\)-algebraic topology over a field
• A cohomological classification of vector bundles on smooth affine threefolds
• On left and right model categories and left and right Bousfield localizations
• On motivic cohomology with \(\mathbb{Z}/l\)-coefficients
• On the suspension triad
• On the suspension sequence
• An exact sequence for \(K^M_*/2\) with applications to quadratic forms
• Milnor-Witt \(K\)-groups of local rings
• The transfer and James-Hopf invariants
• Simplicial presheaves
• Symmetric bilinear forms, quadratic forms and Milnor K-theory in characteristic two
• Topological hypercovers and \(\mathbb{A}^1\)-realizations
• Motivic symmetric spectra
• Étale realization on the \(\mathbb A^1\)-homotopy theory of schemes
• On the powers of the fundamental ideal of a Witt ring
• Reduced power operations in motivic cohomology
• Motivic cohomology with \(\mathbb Z/2\)-coefficients
• Cellular spaces, null spaces and homotopy localization
• The \(K\)-theory of fields in characteristic \(p\)
• Motivic Hopf elements and relations
• A counter-example to the \(\mathbb A^1\)-connectivity conjecture of F. Morel.
• The stable \(\mathbb{A}^1\)-connectivity theorems
• Milnor's conjecture on quadratic forms and mod 2 motivic complexes
• On Hopf invariants
• On the homotopy suspension
• Homotopical algebra
• The generalized Whitehead product
• On adding relations to homotopy groups
• On the Freudenthal theorems
• Cohomologie modulo 2 des complexes d'Eilenberg-MacLane
• On the homotopy groups of unions of spaces
• Reduced product spaces
• Algebraic vector bundles on spheres
• Local Homotopy Theory
• Comparing Euler Classes
• Products and Carrier Theory
• The Stable Suspension of an Eilenberg MacLane Space
• Compositional Methods in Homotopy Groups of Spheres. (AM-49)
• Voevodsky's Lectures on Motivic Cohomology 2000/2001
• Classifying spaces and fibrations
• Splitting vector bundles outside the stable range and 𝔸¹-homotopy sheaves of punctured affine spaces
• An explicit KO‐degree map and applications
• Simplicial homotopy theory
• A generalization of the Hopf invariant
• \(\mathbb{A}^1\)-homotopy theory of schemes

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