Parameterized Lagrangian Floer homotopy

2025/06/25 by Blakey, Kenneth, Bonciocat, Ciprian Mircea
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2506.20122

Abstract

We construct the Lagrangian Floer homotopy type, in the exact setting, as a spectrum parameterized over the moduli space of Maslov data. Our primary motivation for this construction is to provide stronger lower bounds for (possibly degenerate) Lagrangian intersections in plumbings of cotangent bundles.

Citations

• Floer homotopy theory for monotone Lagrangians
• On arborealization, Maslov data, and lack thereof
• Spectral equivalence of nearby Lagrangians
• Spectral Floer theory and tangential structures
• Floer homotopy theory and degenerate Lagrangian intersections
• Revisiting the Cohen-Jones-Segal construction in Morse-Bott theory
• Foundation of Floer homotopy theory I: Flow categories
• Bordism of flow modules and exact Lagrangians
• Equivariant Floer homotopy via Morse-Bott theory
• Lagrangian intersections and cuplength in generalised cohomology theories
• Graded Lagrangian submanifolds

Related

• Floer homotopy theory and degenerate Lagrangian intersections
• Floer homology of Lagrangians in clean intersection
• Local Lagrangian Floer Homology of Quasi-Minimally Degenerate Intersections
• Floer homotopy theory, revisited
• Floer homology via Twisted Loop Spaces