Related papers: Operations on Spaces over Operads and Applications…

We analyze polar actions on Hermitian and quaternion-K\"ahler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries…

First we argue that many BV and homotopy BV structures, including both familiar and new examples, arise from a common underlying construction. The input of this construction is a cyclic operad along with a cyclically invariant Maurer-Cartan…

It is well known that the forgetful functor from symmetric operads to nonsymmetric operads has a left adjoint $Sym_1$ given by product with the symmetric group operad. It is also well known that this functor does not affect the category of…

We establish a braid of interlocking exact sequences containing the group of homotopy self-equivalences of a smooth or topological 4-manifold. The braid is computed for manifolds whose fundamental group is finite of odd order.

In this paper, we investigate the complex symmetric structure of generalized weighted composition operators $D_{m,\psi,\varphi}$ on the weighted Hardy space $H^2(\beta)$. We obtain explicit conditions for $ D_{m,\psi,\varphi}$ to be complex…

Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces $H^p_E(G)$, real Hardy space $H^1_{\mathbb{R}}(G)$, $BMO(G)$, and $BMOA(G)$ for compact Abelian group $G$. Surprisingly, these…

A description of the real, complete modules over the Clifford algebra of a Hilbert space, with the elements of the latter acting by skew-symmetric operators.

We interpret mathematically the pair (master equation, solution of master equation) up to equivalence, as the pair (a presentation of a free triangular dga T over a combination operad O, dga map of T into C, a dga over O) up to homotopy…

We define the concept of a bi-operad. We develop the homotopy theory of "Bital-Sets" and of infinite-bi-operads. We develop a geometry of generalized schemes based on the spectra of distributive monochromatic bi-operads.

In the present work, we realize the space of 2-string links $\mathcal{L}$ as a free algebra over a colored operad denoted $\mathcal{SCL}$ (for "Swiss-Cheese for links"). This result extends works of Burke and Koytcheff about the quotient of…

A new Hopf operad Ram is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad R is introduced on a collection of algebras given by…

We establish a loop space decomposition for certain $CW$-complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of Poincar\'{e} duality complexes in which a loop of a product…

Let $(G,G_1)$ be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces $D_1=G_1/K_1\subset D=G/K$, realized as bounded symmetric domains in complex vector spaces $\mathfrak{p}^+_1\subset\mathfrak{p}^+$…

Operads were originally defined by May to have right actions of the symmetric groups, but later formulations have also used no groups actions at all or group actions by such families as the braid groups. We call such families action…

We study the homology structure of spaces having an action of the \emph{framed disks} operad. In particular, we compute the relations between Kudo-Araki operations and generalized Batalin-Vilkovisky operators. As an application, we complete…

Via a compactification of the cleavage operad, we describe two actions on the mapping spaces from spheres into compact, oriented manifolds. The map from the compactified version of the cleavage operad provides a version of intersection…

We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of a class of solvable Lie groups. We also study compatible co-products by generalizing the notion of smash product…

Starting from any operad P, one can consider on one hand the free operad on P, and on the other hand the Baez--Dolan construction on P. These two new operads have the same space of operations, but with very different notions of arity and…

In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces of deformations. We apply the general…

Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $\pi$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a…