Rabinowitz Floer homology of negative line bundles and Floer Gysin sequence

Albers, Peter; Kang, Jungsoo

doi:10.1016/j.aim.2023.109252

Advances in Mathematics

2023

DOI: 10.1016/j.aim.2023.109252

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Rabinowitz Floer homology of negative line bundles and Floer Gysin sequence

Peter Albers,

Jungsoo Kang

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2024

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Rabinowitz Floer homology for prequantization bundles and Floer Gysin sequence

Bae,

Kang,

Kim

2024

Math. Ann.

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Let Y be a prequantization bundle over a closed spherically monotone symplectic manifold $$\Sigma $$ Σ . Adapting an idea due to Diogo and Lisi, we study a split version of Rabinowitz Floer homology for Y in the following two settings. First, $$\Sigma $$ Σ is a symplectic hyperplane section of a closed symplectic manifold X satisfying a certain monotonicity condition; in this case, $$X {{\setminus }} \Sigma $$ X \ Σ is a Liouville filling of Y. Second, the minimal Chern number of $$\Sigma $$ Σ is greater than one, which is the case where the Rabinowitz Floer homology of the symplectization $$\mathbb {R} \times Y$$ R × Y is defined. In both cases, we construct a Gysin-type exact sequence connecting the Rabinowitz Floer homology of $$X{\setminus }\Sigma $$ X \ Σ or $$\mathbb {R} \times Y$$ R × Y and the quantum homology of $$\Sigma $$ Σ . As applications, we discuss the invertibility of a symplectic hyperplane section class in quantum homology, the isotopy problem for fibered Dehn twists, the orderability problem for prequantization bundles, and the existence of translated points. We also provide computational results based on the exact sequence that we construct.

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Rabinowitz Floer homology for prequantization bundles and Floer Gysin sequence

Bae,

Kang,

Kim

2024

Math. Ann.

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Rabinowitz Floer homology of negative line bundles and Floer Gysin sequence

Cited by 1 publication

References 44 publications

Rabinowitz Floer homology for prequantization bundles and Floer Gysin sequence

Rabinowitz Floer homology for prequantization bundles and Floer Gysin sequence

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