Closed String TCFT for Hermitian Calabi-Yau Elliptic Spaces

Abstract

We describe an explicit action of the prop of the chains on the moduli space of Riemann surfaces on the Hochschild complex of a Calabi-Yau elliptic space. One example of such an elliptic space extends the known string topology operations, for all compact simply-connected manifolds, to a collection indexed by the de Rham currents on the moduli space. Another example pertains to the B-model at all genera.

35 pages

References in corpus (6)

• A polarized view of string topology
• Higher string topology operations
• The Gromov-Witten potential associated to a TCFT
• String Topology: Background and Present State
• The differential topology of loop spaces
• Poincare duality and commutative differential graded algebras