Lagrangian embedding, Maslov indexes and Integer graded symplectic Floer cohomology

1996/02/19 by Weiping Li, Wei-Ping Li, Li, Weiping
Mathematics · #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9602009

24 pages, amslatex

openalex publication_date 1996/02/19 · arxiv created 1996/02/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define an integer graded symplectic Floer cohomology and a spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopies. Such an integer graded Floer cohomology is an integral lifting of the usual Floer-Oh cohomology with Z_{\Si (L)} grading. As one of applications of the spectral sequence, we offer an affirmative answer to an Audin's question for oriented, embedded, monotone Lagrangian tori, i.e. \Si (L) = 2.

Related

• Floer homotopy theory for monotone Lagrangians
• Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds
• Spectral invariants for monotone Lagrangians
• The Maslov class of Lagrangian tori and quantum products in Floer cohomology
• Anchored Lagrangian submanifolds and their Floer theory