Related papers: Homology operations for gravity algebras

Consider a Hamiltonian action of a compact Lie group H on a compact symplectic manifold (M,w) and let G be a subgroup of the diffeomorphism group Diff(M). We develop techniques to decide when the maps on rational homotopy and rational…

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…

Let $G$ be a connected complex semisimple Lie group, $\Gamma$ be a cocompact, irreducible and torsionless lattice in $G$ and $K$ be a maximal compact subgroup of $G$. Assume $\Gamma$ acts by left multiplication and $K$ acts by right…

We provide a homological model for a family of quantum representations of mapping class groups arising from non-semisimple TQFTs (Topological Quantum Field Theories). Our approach gives a new geometric point of view on these…

Using the topological technique of diagrams of spaces, we calculate the homology of the union and the complement of finite arrangements of subspaces of the form $D + SP^{n-d}(X)$ in symmetric products $SP^n(X)$ where $D\in SP^d(X)$. As an…

Let $\phi:\Z/p\to GL_{n}(\Z)$ denote an integral representation of the cyclic group of prime order $p$. This induces a $\Z/p$-action on the torus $X=\R^{n}/\Z^{n}$. The goal of this paper is to explicitly compute the cohomology groups…

A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map \alpha: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples…

The aim of this paper is to make sample computations with the Salvetti complex of the "center of mass" arrangement introduced in [arXiv:math/0611732] by Cohen and Kamiyama. We compute the homology of the Salvetti complex of these…

This thesis studies the pre-quantization of quasi-Hamiltonian group actions from a cohomological viewpoint. The compatibility of pre-quantization with symplectic reduction and the fusion product are established, and are used to understand…

We obtain new calculations of the top weight rational cohomology of the moduli spaces $\mathcal{M}_{2,n}$, equivalently the rational homology of the tropical moduli spaces $\Delta_{2,n}$, as a representation of $S_n$. These calculations are…

Deformation spaces Hom($\pi$,G)/G of representations of the fundamental group $\pi$ of a surface $\Sigma$ in a Lie group $G$ admit natural actions of the mapping class group $Mod_\Sigma$, preserving a Poisson structure. When $G$ is compact,…

In this article we study the homology of spaces ${\rm Hom}(\mathbb{Z}^n,G)$ of ordered pairwise commuting $n$-tuples in a Lie group $G$. We give an explicit formula for the Poincare series of these spaces in terms of invariants of the Weyl…

Let $\mathfrak{g}$ be an untwisted affine Lie algebra with associated Weyl group $W_a$. To any level 0 weight $\gamma$ we associate a weighted graph $\Gamma_\gamma$ that encodes the orbit of $\gamma$ under the action $W_a$. We show that the…

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…

It is well known that a measured groupoid G defines a von Neumann algebra W*(G), and that a Lie groupoid G canonically defines both a C*-algebra C*(G) and a Poisson manifold A*(G). We show that the maps G -> W*(G), G -> C*(G) and G -> A*(G)…

We compute the rank of the first homology group and we study the higher Betti numbers of the real points of the Deligne-Mumford-Knudsen compactification of stable n-pointed curves of genus 0,which coincides with the Chow quotient…

We compute the homology of the matching complex $M(\Gamma)$, where $\Gamma$ is the complete hypergraph on $n\geq 2$ vertices, and analyse the $S_n$-representations carried by this homology. These results are achieved using standard…

Described the algebraic structure on the space of homotopy classes of cycles with marked topological flags of disks. This space is a non-commutative monoid, with an Abelian quotient corresponding to the group of singular homologies…

We study the $E_2$-algebra $\Lambda\mathfrak{M}_{*,1}=\coprod_{g\geqslant 0}\Lambda\mathfrak{M}_{g,1}$ consisting of free loop spaces of moduli spaces of Riemann surfaces with one parametrised boundary component, and compute the homotopy…

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\Z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…