Related papers: Higher Toda brackets and Massey products
We construct Toda brackets in unstable motivic homotopy theory and prove some fundamental properties of them. Furthermore we construct some examples of motivic Toda brackets.
We introduce higher-order Massey products for algebras over algebraic operads. This extends the work of Fernando Muro on secondary ones. We study their basic properties and behavior with respect to morphisms of algebras and operads and give…
In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the…
There are two-dimensional Toda field equations corresponding to each (finite or affine) Lie algebra. The question addressed in this note is whether there exist integrable discrete versions of these. It is shown that for certain algebras…
As part of various obstruction theories, non-trivial Massey products have been studied in symplectic and complex geometry, commutative algebra and topology for a long time. We introduce a general approach to constructing non-trivial Massey…
We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an n-th order track category which is suitable…
In this note I use cup-products and higher Massey products to find topological lower bounds on the number of geometrically distinct critical points of any closed 1-form in a given cohomology class.
The classical deformation theory of Lie algebras involves different kinds of Massey products of cohomology classes. Even the condition of extendibility of an infinitesimal deformation to a formal one-parameter deformation of a Lie algebra…
The exactly integrable systems connected with semisimple series $A$ for arbitrary grading are presented in explicit form. Their general solutions are expressed in terms of the matrix elements of various fundamental representations of $A_n$…
We employ Massey products to find sharper lower bounds for the Schwarz genus of a fibration than those previously known. In particular we give examples of non-formal spaces $X$ for which the topological complexity $\TC(X)$ (defined to be…
Toda equations associated with twisted loop groups are considered. Such equations are specified by Z-gradations of the corresponding twisted loop Lie algebras. The classification of Toda equations related to twisted loop Lie algebras with…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
Motivated by the construction of Steenrod cup-$i$ products in the singular cochain algebra of a space and in the algebra of non-commutative differential forms, we define a category of binomial cup-one differential graded algebras over the…
It is known that a category of many-sorted algebras on pure sets of similarity type is "concretely equivalent" to a category of single-sorted algebras. In this paper, we characterize a single-sorted variety that corresponds to a many-sorted…
A simple procedure to enumerate all Toda systems associated with complex classical Lie groups is given.
We define a new invariant in the homology of a differential graded algebra. This invariant is the obstruction to defining a fourfold Massey product.
In this paper, we give the Jacobi identity of Toda brackets indexed by $n$, ($n \geq 0$), this generalizes Toda's Jacobi identity of Toda brackets indexed by 0 shown in [T].
In the present paper we obtain some integrable generalisations of the continuous Toda system generated by a flat connection form taking values in higher grading subspaces of the algebra of the area--preserving diffeomorphism of the torus…
We study questions inspired by Erd\H os' celebrated distance problems with dot products in lieu of distances, and for more than a single pair of points. In particular, we study point configurations present in large finite point sets in the…
We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.