Higher string topology operations

2007/11/30 by Veronique Godin, Véronique Godin, Godin, Veronique · 6 citations
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Algorithms and Data Compression #Coding theory and cryptography #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0711.4859

78 pages, 12 figures. Typos corrected, some proofs clarified

openalex publication_date 2007/11/30 · arxiv created 2008/02/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Chas and Sullivan have defined an intersection-type product on the homology of the free loop space LM of an oriented manifold M. In this paper we show how to extend this construction to a topological conformal field theory of degree d. In particular, we get operations on the homology of LM which are parameterized by the homology of the moduli space of open-closed Riemann surfaces.

Citations

• The differential topology of loop spaces
• A polarized view of string topology

Cited by

• Renormalization of Chern-Simons Wilson Loops via Flux Quantization in Cohomotopy
• Koszul A-infinity algebras and free loop space homology
• An Algebraic Chain Model of String Topology
• String topology of classifying spaces
• Higher Hochschild cohomology, Brane topology and centralizers of E_n-algebra maps
• String topology with gravitational descendants, and periods of Landau-Ginzburg potentials
• On the homotopy type of the space of Sullivan diagrams
• String Topology: Background and Present State

Related

• Compactifying String Topology
• Open-closed field theories, string topology, and Hochschild homology
• A bordism approach to string topology
• Morse Homotopy and Homological Conformal Field Theory
• On the homology of open-closed string field theory