Rabinowitz Floer homology for Legendrian submanifolds in prequantization bundles

2026/06/30 by Hanwool Bae, Jungsoo Kang, Sungho Kim · 1 voice
Mathematics · #math.SG

paper · pdf

Abstract

Let Y be a prequantization bundle over an integral symplectic manifold (Σ,ω). Let L be a closed monotone Lagrangian submanifold that admits a Legendrian lift L in Y. Under the assumption that the minimal Maslov number N_L of L is greater than 2, we define the Rabinowitz Floer homology of L. We then establish an isomorphism between the ℤ_d-equivariant Rabinowitz Floer homology of L and the quantum homology of L, where d is the degree of the covering map L→ L. Under a more restrictive condition on N_L, we show that this map is a ring isomorphism. Using this isomorphism, we compute the quantum homology ring of Lagrangian spheres in quadrics and two-step flag manifolds. Furthermore, we investigate the implications of the quantum invertibility of ω for the vanishing of the quantum homology of L and the obstructions to topologically simple fillings of L. We also show that if (Σ,ω) admits a polarization and L is disjoint from the Lagrangian trace, the quantum homology of L vanishes.

Discussions

• Hanwool Bae, Jungsoo Kang, Sungho Kim: Rabinowitz Floer homology for Legendrian submanifolds in prequantization bundles https://arxiv.org/abs/2606.31674 https://arxiv.org/pdf/2606.31674 https://arxiv. [bsky, 0 points, 0 comments]

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