On cobordism groups of Lagrangian immersions

2024/09/23 by Dominique Rathel-Fournier, Rathel-Fournier, Dominique
Mathematics · #53D12 #57R90 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2409.14651

openalex publication_date 2024/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the cobordism group Ω^lag(M) of Lagrangian immersions into a symplectic manifold (M, ω) in terms of a stable homotopy group of a Thom spectrum constructed from M. This generalizes a result of Eliashberg in the case of exact symplectic manifolds. As applications, we compute Ω^lag(M) when M is a closed surface and give a partial description of Ω^lag(M) when M is a monotone manifold.

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