相关论文: Higher Homotopy Operations

It is well known that strict $\omega$-categories, strict $\omega$-functors, strict natural $\omega$-transformations, and so on, form a strict $\omega$-category. A similar property for weak $\omega$-categories is one of the main hypotheses…

Higher homotopy generalizations of Lie-Rinehart algebras, Gerstenhaber-, and Batalin-Vilkovisky algebras are explored. These are defined in terms of various antisymmetric bilinear operations satisfying weakened versions of the Jacobi…

We investigate the problem of describing the homotopy classes $[X,Y]$ of continuous functions between $\omega$-bounded non metrizable manifolds $X,Y$. We define a family of surfaces $X$ built with the first octant $C$ in $L^2$ ($L$ is the…

We consider a parameter-dependent version of the homotopy associative part of the Lian-Zuckerman homotopy algebra and provide the interpretation of multilinear operations of this algebra in terms of integrals over certain polytopes. We…

We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The definition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soule, by…

In this paper, we construct groupoid coloured operads governing props and wheeled props, and show they are Koszul. This is accomplished by new biased definitions for (wheeled) props, and an extension of the theory of Groebner bases for…

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…

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.

Closed (and simply-connected) manifolds whose dimensions are greater than 4 are classified via sophisticated algebraic and abstract theory such as surgery theory and homotopy theory. It is difficult to handle 3 or 4-dimensional closed…

We give a construction of homotopy algebras based on ``higher derived brackets''. More precisely, the data include a Lie superalgebra with a projector on an Abelian subalgebra satisfying a certain axiom, and an odd element $\Delta$. Given…

We outline the main features of the definitions and applications of crossed complexes and cubical $\omega$-groupoids with connections. These give forms of higher homotopy groupoids, and new views of basic algebraic topology and the…

We describe a construction that to each algebraically specified notion of higher-dimensional category associates a notion of homomorphism which preserves the categorical structure only up to weakly invertible higher cells. The construction…

For any $r\geq 1$ and $\mathbf{n} \in \mathbb{Z}_{\geq0}^r \setminus \{\mathbf0\}$ we construct a poset $W_{\mathbf{n}}$ called a 2-associahedron. The 2-associahedra arose in symplectic geometry, where they are expected to control maps…

Combinatorial Hopf algebras of trees exemplify the connections between operads and bialgebras. Painted trees were introduced recently as examples of how graded Hopf operads can bequeath Hopf structures upon compositions of coalgebras. We…

We investigate constructions of higher arity self-distributive operations, and give relations between cohomology groups corresponding to operations of different arities. For this purpose we introduce the notion of mutually distributive…

We show that head functions on syntactic objects extend the magma structure to a hypermagma, with the c-command relation compatible with the magma operation and the m-command relation with the hypermagma. We then show that the structure of…

Given a configuration $A$ of $n$ points in $\mathbb{R}^{d-1}$, we introduce the higher secondary polytopes $\Sigma_{A,1},\dots, \Sigma_{A,n-d}$, which have the property that $\Sigma_{A,1}$ agrees with the secondary polytope of…

A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…

We study the relationship between the higher Massey products on the cohomology $H$ of a differential graded algebra, and the $A_\infty$ structures induced on $H$ via homotopy transfer techniques.

We define and study a lift of the Boardman-Vogt tensor product of operads to bimodules over operads.