Related papers: Mapping spaces between operads in relation to bimo…
We study moduli spaces of twisted maps to a smooth pair in arbitrary genus, and give geometric explanations for previously known comparisons between orbifold and logarithmic Gromov--Witten invariants. Namely, we study the space of twisted…
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically…
We consider weighted composition operators, that is operators of the type $g \mapsto w \cdot g \circ f$, acting on spaces of Lipschitz functions. Bounded weighted composition operators, as well as some compact weighted composition…
Given a code from a shift space to an irreducible sofic shift, any two of the following three conditions -- open, constant-to-one, (right or left) closing -- imply the third. If the range is not sofic, then the same result holds when…
We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems…
It is well known since Stasheff's work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads. The…
We introduce a generalization of the notion of operad that we call a contractad, whose set of operations is indexed by connected graphs and whose composition rules are numbered by contractions of connected subgraphs. We show that many…
In this paper, we use the language of operads to study open dynamical systems. More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones. The syntactic architecture of…
Generalizing the approach to pseudo monoidal DG-categories as certain colored non-symmetric DG-operads, we introduce a certain relaxed notion of a category enriched in DG-categories. We construct model structures on the category of colored…
In this paper, we consider boundary extensions of two classes of mappings between metric measure spaces. These two mapping classes extend in particular the well-studied geometric mappings such as quasiregular mappings with integrable…
We give a definition of an operad with general groups of equivariance suitable for use in any symmetric monoidal category with appropriate colimits. We then apply this notion to study the 2-category of algebras over an operad in Cat. We…
We develop the combinatorics of leveled trees in order to construct explicit resolutions of (co)operads and (co)operadic (co)bimodules. We build explicit cofibrant resolutions of operads and operadic bimodules in spectra analogous to the…
We consider a framework for representing double loop spaces (and more generally E-2 spaces) as commutative monoids. There are analogous commutative rectifications of braided monoidal structures and we use this framework to define iterated…
This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…
In this paper, we completely characterize the order boundedness of weighted composition operators between different weighted Dirichlet spaces and different derivative Hardy spaces.
We construct a configuration space model for a particular 2-colored differential graded operad encoding the structure of two $A_\infty$ algebras with two $A_\infty$ morphisms and a homotopy between the morphisms. The cohomology of this…
We argue that operads provide a general framework for dealing with polynomials and combinatory completeness of combinatory algebras, including the classical $\mathbf{SK}$-algebras, linear $\mathbf{BCI}$-algebras, planar…
It is well known that numerical quantities arising from the theory of D-modules are related to invariants of singularities in birational geometry. This paper surveys a deeper relationship between the two areas, where the numerical…
The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix…
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar…