Related papers: Homology operations for gravity algebras

A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…

Let \Sigma = \Sigma _{g,1} be a compact surface of genus g at least 3 with one boundary component, \Gamma its mapping class group and M = H_1(\Sigma , Z) the first integral homology of \Sigma . Using that \Gamma is generated by the Dehn…

In this paper, we investigate the question of how one can recover the homology of a simplicial complex $X$ equipped with a regular action of a finite group $G$ from the structure of its quotient space $X/G.$ Specifically, we describe a…

Given a $\mathfrak{g}$-action on a Poisson manifold $(M, \pi)$ and an equivariant map $J: M \rightarrow \mathfrak{h}^*,$ for $\mathfrak{h}$ a $\mathfrak{g}$-module, we obtain, under natural compatibility and regularity conditions previously…

We compute the homology of the space of equivariant loops on the classifying space of a simplicial monoid $M$ with anti-involution, provided $\pi_0 (M)$ is central in the homology ring of $M$. The proof is similar to McDuff and Segal's…

In this work we study riemannian metrics on flag manifolds adapted to the symmetries of these homogeneous nonsymmetric spaces. We first introduce the notion of riemannian $\Gamma $-symmetric space when $\Gamma $ is a general abelian finite…

This paper studies Hamiltonian circle actions, i.e. circle subgroups of the group Ham(M,\om) of Hamiltonian symplectomorphisms of a closed symplectic manifold (M,\om). Our main tool is the Seidel representation of \pi_1(\Ham(M,\om)) in the…

Let ${\cal O}$ be a quantizable coadjoint orbit of a semisimple Lie group $G$. Under certain hypotheses we prove that $#(\pi_1(\text{Ham}({\cal O})))\geq #(Z(G))$, where $\text{Ham}({\cal O})$ is the group of Hamiltonian symplectomorphisms…

Let X be a topological space. The homology of the iterated loop space $H_*\Omega^n X$ is an algebra over the homology of the framed n-disks operad $H_*f\mathcal{D}_n$ \cite{Getzler:BVAlg,Salvatore-Wahl:FrameddoBVa}. We determine completely…

In the present paper the cyclic homology functor from the category of $A_\infty$-algebras over any commutative unital ring $K$ to the category of graded $K$-modules is constructed. Further, it is showed that this functor sends homotopy…

In this chapter we give a geometric representation of $H_{n}(B;\mathbb{L})$ classes, where $\mathbb{L}$ is the $4$-periodic surgery spectrum, by establishing a relationship between the normal cobordism classes…

We show by studying the symplectic geometry of the extended moduli space that the intersection cohomology of the representation space $Hom(\pi_1(\Sigma),G)/G$ for a simply connected compact Lie group $G$ is naturally embedded into the $G$…

The observation that a graph of rank $n$ can be assembled from graphs of smaller rank $k$ with $s$ leaves by pairing the leaves together leads to a process for assembling homology classes for $Out(F_n)$ and $Aut(F_n)$ from classes for…

In this paper we study homotopy type of certain moduli spaces of metric graphs. More precisely, we show that the spaces $MG_{1,n}^v$, which parametrize the isometry classes of metric graphs of genus 1 with $n$ marks on vertices are homotopy…

Let $M_n$ be the configuration space of equilateral polygonal linkages with $n$ vertices in the Euclidean plane ${\mathbb R}^2$. We consider the case that $n$ is odd and set $n=2m+1$. In spite of the long history of research, the homology…

In the present note we describe a family of $H^*$-algebra structures on the set $ L^2(X)$ of square integrable functions on a rank-one para-Hermitian symmetric space $X$.

Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using…

Given a Lie group acting on a manifold $M$ preserving a closed $n+1$-form $\omega$, the notion of homotopy moment map for this action was introduced in Callies-Fregier-Rogers-Zambon [6], in terms of $L_{\infty}$-algebra morphisms. In this…

In this paper we study the topology of the space of Riemann surfaces in a simply connected space X, S_{g,n} (X, \gamma). This is the space consisting of triples, (F_{g,n}, \phi, f), where F_{g,n} is a Riemann surface of genus g and…