Noncommutative aspects of open/closed strings via foliations

Abstract

We give a brief summary of algebraic aspects of string theory arising in the noncommutative geometry setting of foliations called string diagrammatics which we introduced jointly with Bob Penner. We furthermore discuss how this gives rise to actions on the Hochschild complex of a Frobenius algebra. We then explain how this leads to new quantum chains for loop spaces and a stabilization in the semi--simple case.

12 pages 3 figures. ROMP to appear

References in corpus (8)

• On the structure of open-closed topological field theory in two dimensions
• Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras
• On the relation between open and closed topological strings
• Arc Operads and Arc Algebras
• Closed/open string diagrammatics
• Higher Weil-Petersson Volumes of Moduli Spaces of Stable $n$-pointed Curves
• Probing mapping class groups using arcs
• Second quantized Frobenius algebras

Cited by in corpus (2)

• Open/Closed String Topology and Moduli Space Actions via Open/Closed Hochschild Actions
• A finitely presented $E_{\infty }$-prop II: cellular context