Morse-Bott split symplectic homology

• We associate a chain complex to a Liouville domain ((W) over bar ,d lambda) whose boundary Y admits a Boothby-Wang contact form (i.e.is a prequantization space). The differential counts Floer cylinders with cascades in the completion W of (W) over bar, in the spirit of Morse-Bott homology (Bourgeois in A Morse-Bott approach to contact homology, Ph.D. Thesis. ProQuest LLC, Stanford University, Ann Arbor 2002; Frauenfelder in Int Math Res Notices 42:2179-2269, 2004; Bourgeois and Oancea in Duke Math J 146(1), 71-174, 2009). The homology of this complex is the symplectic homology of W (Diogo and Lisi in J Topol 12:966-1029, 2019). Let X be obtained from (W) over bar by collapsing the boundary Y along Reeb orbits, giving a codimension two symplectic submanifold Sigma. Under monotonicity assumptions on X and Sigma, we show that for generic data, the differential in our chain complex counts elements of moduli spaces of cascades that are transverse. Furthermore, by some index estimates, we show that very few combinatorial types of cascades can appear in the differential.

Subject headings

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

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ref (subject category)

art (subject category)