Twisted IBL-infinity-algebra and string topology: First look and examples

Abstract

We study the application of IBL-infinity-algebras to string topology and explicitly compute the case of spheres. This involves finding a Green kernel and computing integrals associated to trivalent ribbon graphs, which are similar to integrals from perturbative Chern-Simons theory. We generalize the computation and show that the twisted IBL-infinity-structure in question is in many cases trivial.

arXiv commentNew version from January, 2019: a general vanishing result for the Maurer-Cartan element due to a tricky Green kernel modification from "A. Cattaneo, P. Mnev, Remarks on Chern-Simons theory"; more precise formulation of the string topology conjecture; other minor changes

References in corpus (8)

• String Topology
• Remarks on Chern-Simons invariants
• Quantum Open-Closed Homotopy Algebra and String Field Theory
• Homological algebra related to surfaces with boundary
• Algebra+Homotopy=Operad
• Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory
• A primer on A-infinity-algebras and their Hochschild homology
• Properads and Homotopy Algebras Related to Surfaces

Cited by in corpus (2)

• IBL-Infinity Model of String Topology from Perturbative Chern-Simons Theory
• Cumulants, Koszul brackets and homological perturbation theory for commutative $B{V}_{\infty }$ and $IB{L}_{\infty }$ algebras