Open-closed Deligne-Mumford field theories: geometric foundations

TL;DR

This paper develops the geometric foundations for open-closed Deligne-Mumford field theories by constructing global Kuranishi charts for moduli spaces of pseudo-holomorphic maps with boundary, enabling chain-level operations.

Contribution

It introduces a method to construct global Kuranishi charts for moduli spaces of pseudo-holomorphic maps with boundary, foundational for open-closed field theories.

Findings

Constructed global Kuranishi charts for moduli spaces of pseudo-holomorphic maps.

Established geometric foundations for chain-level operations in open-closed theories.

Facilitated the development of an open-closed Deligne-Mumford field theory.

Abstract

We construct global Kuranishi charts for moduli spaces of pseudo-holomorphic maps of arbitrary genus with boundary on an embedded Lagrangian submanifold. We then build the geometric foundations required for obtaining compatible chain-level operations, which are employed in follow-up work to construct an open-closed Deligne-Mumford field theory.