On the homology of open-closed string field theory

TL;DR

This paper computes the homology of a 2-colored dioperad related to open-closed string field theory and demonstrates its realization in open-closed string topology through an action on topological spaces.

Contribution

It provides the first explicit computation of the homology of a dioperad relevant to open-closed string field theory and connects it to string topology.

Findings

Homology of the dioperad is explicitly computed.

The structure is realized via an action in open-closed string topology.

Connects algebraic structures to topological actions.

Abstract

The homology of a 2-colored dioperad of decorated Riemann surfaces, relevant to open-closed string field theory, is computed. The structure it describes is realized in an open-closed setting of string topology via an action at the level of topological spaces.