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arxiv: 2501.04687 · v2 · submitted 2025-01-08 · 🧮 math.SG

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Open-closed Deligne-Mumford field theories: geometric foundations

Amanda Hirschi , Kai Hugtenburg
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classification 🧮 math.SG
keywords constructdeligne-mumfordfieldfoundationsgeometricopen-closedarbitraryboundary
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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.

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  1. The topology of Lagrangian submanifolds via open-closed string topology

    math.SG 2026-04 unverdicted novelty 5.0

    A curved deformation of the dg algebra on the based loop space of L is built from holomorphic disc moduli spaces via string topology, implying non-vanishing Maslov class when pi2(L) vanishes.