Related papers: On string topology of classifying spaces

Twenty years ago, Mumford initiated the systematic study of the cohomology ring of moduli spaces of Riemann surfaces. Around the same time, Harer proved that the homology of the mapping class groups of oriented surfaces is independent of…

We prove the decomposition theorem for the loop homotopy algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix.…

This paper, in a sense, completes a series of three papers. In the previous two hep-th/0404013, hep-th/0410293, we have explored the possibility of refining the K-theory partition function in type II string theories using elliptic…

We study string topology for classifying spaces of connected compact Lie groups, drawing connections with Hochschild cohomology and equivariant homotopy theory. First, for a compact Lie group $G$, we show that the string topology…

Let M be a closed, oriented, n -manifold, and LM its free loop space. Chas and Sullivan defined a commutative algebra structure in the homology of LM, and a Lie algebra structure in its equivariant homology. These structures are known as…

We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…

We classify the topological terms (in a sense to be made precise) that may appear in a non-linear sigma model based on maps from an arbitrary worldvolume manifold to a homogeneous space $G/H$ (where $G$ is an arbitrary Lie group and $H…

We introduce a symmetric monoidal $\infty$-category $\mathrm{GrCob}$ of graph cobordisms between spaces, and use the homology of its morphism spaces to define string operations. Precisely, for an $E_\infty$-ring spectrum $R$ and an oriented…

By studying spaces of flow graphs in a closed oriented manifold, we construct operations on its cohomology, parametrized by the homology of the moduli spaces of compact Riemann surfaces with boundary marked points. We show that the…

We study properties of differential graded (dg) operads modulo weak equivalences, that is, modulo the relation given by the existence of a chain of dg operad maps inducing a homology isomorphism. This approach, naturally arising in string…

We revisit the existence, background independence and uniqueness of closed, open and open-closed bosonic- and topological string field theory, using the machinery of homotopy algebra. In a theory of classical open- and closed strings, the…

We show that in closed string topology and in open-closed string topology with one $D$-brane, higher genus stable string operations are trivial. This is a consequence of Harer's stability theorem and related stability results on the…

In this manuscript, we investigate a Cartan calculus on the homology of free loop spaces which is introduced by Kuribayashi, Wakatsuki, Yamaguchi and the author. In particular, it is proved that the Cartan calculus can be described by the…

$A_\infty$ categories are a mathematical structure that appears in topological field theory, string topology, and symplectic topology. This paper studies the cyclic homology of a Calabi-Yau $A_\infty$ category, and shows that it is…

We study a spectral sequence that computes the (mod 2) S^1-equivariant homology of the free loop space LM of a manifold M (the "string homology" of M). Using it and knowledge of the string topology operations on the homology of LM, we…

The homology of the free and the based loop space of a compact globally symmetric space can be studied through explicit cycles. We use cycles constructed by Bott and Samelson and by Ziller to study the string topology coproduct and the…

This paper is an exposition of the new subject of String Topology. We present an introduction to this exciting new area, as well as a survey of some of the latest developments, and our views about future directions of research. We begin…

In this paper we use trivial defects to define global taffy-like operations on string worldsheets, which preserve the field theory. We fold open and closed strings on a space X into open strings on products of multiple copies of X, and…

This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…

In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic…