A symplectic Gysin sequence

Abstract

We use the theory of pseudo-holomorphic quilts to establish a counterpart, in symplectic Floer homology, to the Gysin sequence for the homology of a sphere-bundle. In a motivating class of examples, this "symplectic Gysin sequence" is precisely analogous to an exact sequence describing the behaviour of Seiberg-Witten monopole Floer homology for 3-manifolds under connected sum.

62 pages, 6 figures

References in corpus (2)

• Quantum Structures for Lagrangian Submanifolds
• Lagrangian matching invariants for fibred four-manifolds: II

Cited by in corpus (11)

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• Fukaya Categories as Categorical Morse Homology
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• Projective twists and the Hopf correspondence
• Floer cohomology and pencils of quadrics
• Translated points for contactomorphisms of prequantization spaces over monotone symplectic toric manifolds
• Geometric composition in quilted Floer theory
• Traceless Character Varieties, the Link Surgeries Spectral Sequence, and Khovanov Homology