Morse homotopy and topological conformal field theory

Abstract

By studying spaces of flow graphs in a closed oriented manifold, we equip the Morse complex with the operations of an open topological conformal field theory. This complements previous constructions due to R. Cohen et al., K. Costello, K. Fukaya and M. Kontsevich and is also the Morse theoretic counterpart to a conjectural construction of operations on the chain complex of the Lagrangian Floer homology of the zero section of a cotangent bundle, obtained by studying uncompactified moduli spaces of higher genus pseudoholomorphic curves.