Related papers: Free loop space and homology

A free massless scalar field is coupled to homogeneous and isotropic loop quantum cosmology. The coupled model is investigated in the vicinity of the classical singularity, where discreteness is essential and where the quantum model is…

Using Nadler's Geometric Satake Equivalence for real reductive groups, we obtain a description of the equivariant homology of the loop space of splitting-rank symmetric spaces in terms of the relative dual group of the space. The…

The purpose of this note is to extend to Brownian loops some homology and holonomy results obtained in the case of discrete loops on a graph

We give a homotopy equivalence for the loop space of the moment-angle complex associated with a simplicial complex formed by the polyhedral join operation, and give necessary conditions for this loop space to be a finite type product of…

F\'{e}lix and Thomas developed string topology of Chas and Sullivan on simply-connected Gorenstein spaces. In this paper, we prove that the degree shifted homology of the free loop space of a simply-connected ${\mathbb Q}$-Gorenstein space…

We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a ``cohomology theory" for complex algebraic varieties. The theory is bigraded, functorial,…

In this article, we pursue the study begun in \cite{Lup02} on the cohomology of rationally elliptic coformal spaces. Consequently, we complete, for such spaces, the proof of Lupton's conjecture and deduce Hilali's.

Let $X$ be a finitistic space with the mod 2 cohomology of the product space of a projective space and a 4-sphere. Assume that $X$ admits a free involution. In this paper we study the mod 2 cohomology algebra of the quotient of $X$ by the…

We study the topology of some simple infinite dimensional singularities arising from spaces of \emph{algebraic formal loops}. We prove that in some simple cases the natural analogue of nearby cycles cohomology for a function on the loop…

This is primarily a survey of the way in which Hopf cyclic cohomology has emerged and evolved, in close relationship with the application of the noncommutative local index formula to transverse index theory on foliations. Being…

We show that the Hochschild cohomology of a monomial algebra over a field of characteristic zero vanishes from degree two if the first Hochschild cohomology is semisimple as a Lie algebra. We also prove that first Hochschild cohomology of a…

A stable homology theory is defined for completely distributive CSL algebras in terms of the point-neighbourhood homology of the partially ordered set of meet-irreducible elements of the invariant projection lattice. This specialises to the…

The loop homology of a closed orientable manifold $M$ of dimension $d$ is the ordinary homology of the free loop space $M^{S^1}$ with degrees shifted by $d$, i.e. $\mathbb H_*(M^{S^1}) = H_{*+d}(M^{S^1})$. Chas and Sullivan have defined a…

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be…

Recently R. Cohen and V. Godin have proved that the homology of the free loop space of a closed oriented manifold with coefficients in a field has the structure of a Frobenius algebra without counit. In this short note we prove that when…

Growth of the Hilbert-Poincar\"e series for the rational homology of the free loop space of a toric space is addressed. In case the toric space is a manifold, the structure of the fan dictates whether the Hilbert-Poincar\"e series has…

In this paper we study the homology and cohomology of confguration spaces of two distinct particles on a graph. Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra of the…

By a result of Gerstenhaber and Schack the simplicial cohomology ring $H^*(\mathcal{C};k)$ of a poset $\mathcal{C}$ is isomorphic to the Hochschild cohomology ring $HH^*(k\mathcal{C})$ of the category algebra $k\mathcal{C}$, where the poset…

In this paper we explore the relations between the Hochschild cohomology of an algebra over some field and the Hochschild cohomology of its smash product with a finite group. Basically we are concentrated on the case where the group under…

We establish the relationship between the cohomology of a certain sheaf on the intersection lattice of a hyperplane arrangement introduced by Yuzvinsky and the cohomology of the coherent sheaf on punctured affine space, respectively…