Related papers: Explicit Homotopy Equivalences Between Some Operad…
We show that for a weighted Lipschitz operator $\omega\widehat{f}$, certain linear properties are equivalent. Specifically, we prove that compactness, strict singularity, and strict cosingularity are all equivalent to the property of not…
We study a compactification of the configuration space of n distinct labeled points on an arbitrary nonsingular variety. Our construction provides a generalization of the original Fulton-MacPherson compactification that is parallel to the…
We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex…
We compute the structure of the homology of an operad built from the spaces TH_{d,n} of configurations of points in C^d, modulo translation and homothety. We find that it is a mild generalization of Getzler's gravity operad, which occurs in…
A well-known construction of associahedra comes from truncations of simplices. Motivated by compactifications of point configurations, we show associahedra as truncations of certain products of simplices. This is then used to provide a…
Our main result is a recognition principle for iterated suspensions as coalgebras over the little disks operads. Given a topological operad, we construct a comonad in pointed topological spaces endowed with the wedge product. We then prove…
It was shown in a recent paper by Boavida de Brito and Weiss that a well-known construction which to a plain (=monochromatic) topological operad associates a topological category and a functor from it to the category of finite sets is…
In this work, we prove that weak compactness of composition operator on $H^{1}(U^{n})$ coincides with its compactness. We also characterize bounded and compact composition operators on $H^{1}(U^{n}).$\
In this paper, we generalize the Dunn-Brinkmeier~additivity theorem, which establishes a weak equivalence $\mathcal{C}_n \otimes \mathcal{C}_m \simeq \mathcal{C}_{n+m}$ for the little cubes operad $\mathcal{C}_n$. We introduce equivariant…
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…
The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked points and nodes. We show that this cyclic operad is formal,…
Conditions for a composition operator on the Hardy space of the disk to have closed range or be similar to an isometry are well known. We provide such conditions for composition operators on the Hardy space of the upper half-plane. We also…
We study the operad structure on the homology of moduli spaces of pointed rooted trees of $d$-dimensional projective spaces, introduced by Chen, Gibney and Krashen a couple of decades ago. We describe this operad by generators and…
In the present work, we extract pairs of topological spaces from maps between coloured operads. We prove that those pairs are weakly equivalent to explicit algebras over the one dimensional Swiss-Cheese operad SC_{1}. Thereafter, we show…
We study homotopy-coherent commutative multiplicative structures on equivariant spaces and spectra. We define N-infinity operads, equivariant generalizations of E-infinity operads. Algebras in equivariant spectra over an N-infinity operad…
The d.g. operad C of cellular chains on the operad of spineless cacti is isomorphic to the Gerstenhaber-Voronov operad codifying the cup product and brace operations on the Hochschild cochains of an associative algebra, and to the suboperad…
We provide general conditions under which the algebras for a coloured operad in a monoidal model category carry a Quillen model structure, and prove a Comparison Theorem to the effect that a weak equivalence between suitable such operads…
We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate…
We show, by an elementary and explicit construction, that the group of Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of arbitrary dimension.
As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or on a circle. The construction of the compactification endows…