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Related papers: Higher string topology operations

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This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a…

Quantum Algebra · Mathematics 2014-11-11 Kevin J. Costello

We show that any open 2-dimensional topological field theory valued in a symmetric monoidal $\infty$-category (with suitable colimits) extends canonically to an open-closed field theory whose value at the circle is the Hochschild homology…

Algebraic Topology · Mathematics 2025-10-28 Shaul Barkan , Jan Steinebrunner , Adela YiYu Zhang

String backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal's definition of a conformal field theory. Relations with conformal field theory, topological field theory and…

High Energy Physics - Theory · Physics 2008-02-03 Alexander A. Voronov

We extend the structure of string topology from mapping spaces to embedding spaces $Emb(S^n,M)$. This extension comes from an action of the cleavage operad, a coloured $E_{n+1}$-operad. For all values of $n \in \mathbb{N}$, this gives an…

Algebraic Topology · Mathematics 2015-08-10 Tarje Bargheer

The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented $C^\infty$-manifold. For this purpose, we define a (nonsymmetric)…

Geometric Topology · Mathematics 2017-02-14 Kei Irie

We calculate the homology of the free loop space of (n-1)-connected closed manifolds of dimension at most 3n-2 (n > 1), with the Chas-Sullivan loop product and loop bracket. Over a field of characteristic zero, we obtain an expression for…

Algebraic Topology · Mathematics 2015-02-12 Alexander Berglund , Kaj Börjeson

In this article we consider algebraic structures on the homology of the space of paths in a manifold with endpoints in a submanifold. The Pontryagin-Chas-Sullivan product on the homology of this space had already been investigated by…

Algebraic Topology · Mathematics 2025-02-11 Maximilian Stegemeyer

Recent algebraic structures of string theory, including homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras, are deduced from the topology of the moduli spaces of punctured Riemann spheres. The principal reason for these…

High Energy Physics - Theory · Physics 2009-10-22 T. Kimura , J. Stasheff , A. A. Voronov

In this note, we first explain the equivalence between the interaction Hamiltonian of Green-Schwarz light-cone gauge superstring field theory and the twist field formalism known from matrix string theory. We analyze the role of the large N…

High Energy Physics - Theory · Physics 2007-05-23 Robbert Dijkgraaf , Lubos Motl

We study the homology of free loop spaces via techniques arising from the theory of topological coHochschild homology (coTHH). Topological coHochschild homology is a topological analogue of the classical theory of coHochschild homology for…

Algebraic Topology · Mathematics 2021-12-15 Anna Marie Bohmann , Teena Gerhardt , Brooke Shipley

In this paper, we use Chas-Sullivan theory on loop homology and Leray-Serre spectral sequence to investigate the topological structure of the non-contractible component of the free loop space on the real projective spaces with odd…

Geometric Topology · Mathematics 2015-03-25 Yuming Xiao , Yiming Long

Given a space with a circle action, we study certain cocyclic chain complexes and prove a theorem relating cyclic homology to $S^1$-equivariant homology, in the spirit of celebrated work of Jones. As an application, we describe a chain…

Algebraic Topology · Mathematics 2024-02-07 Yi Wang

We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f: X->BF, where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of…

Algebraic Topology · Mathematics 2014-11-11 A. J. Blumberg , R. L. Cohen , C. Schlichtkrull

The string topology coproduct on the homology of the free loop space of a closed manifold induces a string cobracket on $S^1$-equivariant homology. We give a complete computation of the string topology coproduct for surfaces of higher genus…

Algebraic Topology · Mathematics 2025-10-08 Jana Hartenstein , Maximilian Stegemeyer

We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.

High Energy Physics - Theory · Physics 2008-11-26 Mauro Carfora , Claudio Dappiaggi , Valeria L. Gili

The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant…

High Energy Physics - Theory · Physics 2026-05-07 P. T. Kirakosiants

Let M be a closed, connected manifold, and LM its loop space. In this paper we describe closed string topology operations in h_*(LM), where h_* is a generalized homology theory that supports an orientation of M. We will show that these…

Algebraic Topology · Mathematics 2007-05-23 Ralph L. Cohen , Veronique Godin

We introduce various versions of spin structures on free loop spaces of smooth manifolds, based on a classical notion due to Killingback, and additionally coupled to two relations between loops: thin homotopies and loop fusion. The central…

Differential Geometry · Mathematics 2015-08-07 Konrad Waldorf

We establish the general machinery of string topology for differentiable stacks. This machinery allows us to treat on an equal footing free loops in stacks and hidden loops. In particular, we give a good notion of a free loop stack, and of…

Algebraic Topology · Mathematics 2011-01-05 Kai Behrend , Grégory Ginot , Behrang Noohi , Ping Xu

In this paper we define and study the moduli space of metric-graph-flows in a manifold M. This is a space of smooth maps from a finite graph to M, which, when restricted to each edge, is a gradient flow line of a smooth (and generically…

Geometric Topology · Mathematics 2007-05-23 Ralph L. Cohen , Paul Norbury