Related papers: Motivic Toda brackets

We construct more non-trivial examples for Toda brackets in unstable motivic homotopy theory via the first and second motivic Hopf maps.

We define subscripted unstable higher Toda brackets and study their elementary properties. This paper is the continuation of our previous paper in which we defined the non-subscripted unstable higher Toda brackets.

We show that a system of unstable higher Toda brackets can be defined inductively.

We provide a general definition of Toda brackets in a pointed model categories, show how they serve as obstructions to rectification, and explain their relation to the classical stable operations.

We define inductively unstable n-fold Toda brackets for every n>2 in the category of spaces with base points, and then define stable ones.

We describe two ways to define higher order Toda brackets in a pointed simplicial model category $\mathcal{D}$: one is a recursive definition using model categorical constructions, and the second uses the associated simplicial enrichment.…

In this expository article, we give the foundations, basic facts, and first examples of unstable motivic homotopy theory with a view towards the approach of Asok-Fasel to the classification of vector bundles on smooth complex affine…

In this paper we introduce and study motives for rational homotopy types.

This is an expository paper providing an overview of the unstable motivic homotopy category using the theory of $(\infty,1)$-categories. In this paper, we examine two constructions in the literature and discuss their equivalence.

We give two formulas for the generalized Hopf invariant and 4-fold Toda brackets which are useful in computations of homotopy groups of spheres.

We define two new unstable n-fold Toda brackets for every composable sequence (f_n, ... ,f_1) of pointed maps f_i : X_i \to X_{i+1} between well-pointed spaces with n > 2. The brackets agree with the classical Toda bracket when n = 3, and…

We give an introduction to unstable motivic homotopy theory of Morel and Voevodsky, and survey some results.

These notes, written version of a Bourbaki talk, survey Morel-Voevodsky's motivic homotopy theory over a field, with a focus on computations of motivic homotopy sheaves, both stable and unstable. We also describe Isaksen-Wang-Xu's…

We construct and examine the universal Toda bracket of a highly structured ring spectrum R. This invariant of R is a cohomology class in the Mac Lane cohomology of the graded ring of homotopy groups of R which carries information about R…

In this paper, we give an unstable approach of the May-Lawrence matrix Toda bracket, which becomes a useful tool for the theory of determinations of unstable homotopy groups. Then, we give a generalization of the classical isomorphisms…

Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…

This paper tackles \textit{N. Oda}'s extension problems for the homotopy groups $\pi_{39}(S^{6})$, $\pi_{40}(S^{7})$, and $\pi_{41}(S^{8})$ localized at 2, the issues having eluded resolution for more than four decades. We introduce a tool…

We prove that for any base scheme $S$, real \'etale motivic (unstable) homotopy theory over $S$ coincides with unstable semialgebraic topology over $S$ (that is, sheaves of spaces on the real spectrum of $S$). Moreover we show that for…

Building on earlier work concerning the motives of $G$-bundles, we study the structure of motives associated with certain classes of $G$-varieties. In particular, we show that the corresponding motives lie within the category of mixed-Tate…

The term "motivic Moore spectrum" refers to a cone of an element in the motivic stable homotopy groups of spheres. This article discusses some properties of motivic Moore spectra, among them the question whether the ring structure on the…