Related papers: The loop group and the cobar construction

Let (G,G^+) be a simple ordered abelian group. We say that G has strong perforation if there exists a non-positive element x in G such that nx is positive and non-zero for some natural number n. Otherwise, the group is said to be weakly…

We know that any element $X$ of the exceptional Jordan algebra $\gJ$ is transformed to a diagonal form by the compact exceptional Lie group $F_4$. However, its proof is used the method which is reduced a contradiction. In this paper, we…

Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of…

We construct a many-object dual version of Chen's iterated integral map. For any topological space X, the construction takes the form of an A-infinity functor between two dg categories whose objects are the points of X: the domain has as…

Aiming for a revival of the theory of crystallographic complex reflection groups, we compute (minimal) Coxeter-like reflection presentations for the infinite families of those non-genuine groups which satisfy Steinberg's fixed point…

Given a manifold with corners $X$, we associates to it the corner structure simplicial complex $\Sigma_X$. Its reduced K-homology is isomorphic to the K-theory of the $C^*$-algebra $\mathcal{K}_b(X)$ of b-compact operators on $X$. Moreover,…

If $X$ is a projective variety and $G$ is an algebraic group acting algebraically on $X$, we provide a counter-example to the existence of a $G$-equivariant extension on the formal semi-universal deformation of $X$.

Let $X$ be a simply connected space and $\Bbb K$ be any field. The normalized singular cochains $N^*(X; {\Bbb K})$ admit a natural strongly homotopy commutative algebra structure, which induces a natural product on the Hochschild homology…

Assume that we are given a coaction \delta of a locally compact group G on a C*-algebra A and a T-valued Borel 2-cocycle \omega on G. Motivated by the approach of Kasprzak to Rieffel's deformation we define a deformation A_\omega of A.…

We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…

Let $M$ be a smooth manifold, smoothly triangulated by a simplicial complex $K$, and $\cA$ a transitive Lie algebroid on $M$. The Lie algebroid restriction of $\cA$ to a simplex $\Delta$ of $K$ is denoted by $\cA^{!!}_{\Delta}$. A piecewise…

For $G$ an algebraic group definable over a model of $\operatorname{ACVF}$, or more generally a definable subgroup of an algebraic group, we study the stable completion $\widehat{G}$ of $G$, as introduced by Loeser and the second author.…

We examine a condition on a simply connected 2-complex X ensuring that groups acting properly on X are coherent. This extends earlier work on 2-complexes with negative sectional curvature which covers the case that G acts freely. Our…

We study deformation of algebras with coaction symmetry of reduced algebra of discrete groups, where the deformation parameter is given continuous family of group $2$-cocycles. When the group satisfies the Baum-Connes conjecture with…

In this paper, we firstly construct an $L_\infty[1]$-algebra via the method of higher derived brackets, whose Maurer-Cartan elements correspond to relative $\Omega$-family Rota-Baxter algebras structures of weight $\lambda$. For a relative…

In this thesis we give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. In his seminal book, Connes constructs a map from the equivariant cohomology of a manifold carrying the…

Let G be a connected reductive complex algebraic group acting on a smooth complete complex algebraic variety X. We assume that X under the action of G is a regular embedding, a condition satisfied in particular by smooth toric varieties and…

Let $(W,S)$ be a Coxeter system and $\Gamma$ be a group of automorphisms of $W$ such that $\gamma(S)=S$ for all $\gamma \in \Gamma$. Then it is known that the group of fixed points $W^\Gamma$ is again a Coxeter group with a canonically…

We extend the Cox-Hu-Keel construction of the Cox rings to any proper birational morphisms of normal noetherian schemes. It allows the representation of any proper birational morphism by a map of schemes with mild singularities with torus…

This paper proves that the homotopy type of a pointed, simply-connected, 2-reduced simplicial set is determined by the chain-complex augmented by functorial diagonal and higher diagonal maps (a simple generalization of the ones used to…