Related papers: Swiss-Cheese operad and Drinfeld center
A new topological operad is introduced, called the splicing operad. This operad acts on a broad class of spaces of self-embeddings N --> N where N is a manifold. The action of this operad on EC(j,M) (self embeddings R^j x M --> R^j x M with…
We establish a surgery formula for 3-dimensional Seiberg-Witten monopoles under (+1) Dehn surgery on a knot in a homology 3-sphere. (substantial revision)
We construct a new (cyclic) operad of `mosaics' defined by polygons with marked diagonals. Its underlying (aspherical) spaces are the sets of real points of the moduli space of punctured Riemann spheres, which are naturally tiled by…
In this paper, we set up a rational homotopy theory for operads in simplicial sets whose term of arity one is not necessarily reduced to an operadic unit, extending results obtained by the author in the book "Homotopy of operads and…
We develop here a concept of deformed algebras and their related groups through two examples. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of…
In this paper we study the category of braided categorical Leibniz algebras and braided crossed modules of Leibniz algebras and we relate these structures with the categories of braided categorical Lie algebras and braided crossed modules…
The difference between slice and doubly-slice knots is reflected in algebra by the difference between metabolic and hyperbolic Blanchfield linking forms. We exploit this algebraic distinction to refine the classical Witt group of linking…
It is proven that a matched pair of actions on a Hopf algebra $H$ is equivalent to the datum of a Yetter-Drinfeld brace, which is a novel structure generalising Hopf braces. This improves a theorem by Angiono, Galindo and Vendramin,…
We introduce the graded bialgebra deformations, which explain Andruskiewitsch-Schneider's liftings method. We also relate this graded bialgebra deformation with the corresponding graded bialgebra cohomology groups, which is the graded…
In this paper, we present Sch\"utzenberger's factorization in different combinatorial contexts and show that its validity is not restricted to these cases but can be extended to every Lie algebra endowed with an ordered basis. We also…
We construct quasi-Hopf algebras quantizing double extensions of the Manin pairs of Drinfeld, associated to a curve with a meromorphic differential, and the Lie algebra sl(2). This construction makes use of an analysis of the vertex…
We explain how the theory of sandwich cellular algebras can be seen as a version of cell theory for algebras. We apply this theory to many examples such as Hecke algebras, and various monoid and diagram algebras.
Several topological and homological operads based on families of projectively weighted arcs in bounded surfaces are introduced and studied. The spaces underlying the basic operad are identified with open subsets of a compactification due to…
In this paper, first we construct a Lie 2-algebra associated to every Leibniz algebra via the skew-symmetrization. Furthermore, we introduce the notion of the naive representation for a Leibniz algebra in order to realize the abstract…
Based on a relative Wu theorem in \'etale cohomology, we study the compatibility of Steenrod operations on Chow groups and on \'etale cohomology. Using the resulting obstructions to algebraicity, we construct new examples of non-algebraic…
Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…
Given an action $\varphi$ of of inverse semigroup $S$ on a ring $A$ (with domain of $\varphi(s)$ denoted by $D_{s^*}$) we show that if the ideals $D_e$, with $e$ an idempotent, are unital, then the skew inverse semigroup ring $A\rtimes S$…
We generalize quantum Drinfeld Hecke algebras by incorporating a 2-cocycle on the associated finite group. We identify these algebras as specializations of deformations of twisted skew group algebras, giving an explicit connection to…
We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of…
We extend the classical Poincar\'e-Birkhoff-Witt theorem to higher algebra by establishing a version that applies to spectral Lie algebras. We deduce this statement from a basic relation between operads in spectra: the commutative operad is…