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Morse-Bott split symplectic homology
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Univ Fed Fluminense, Inst Matemat & Estat, Rua Prof Marcos Waldemar de Freitas Reis S-N, BR-24210201 Niteroi, RJ, Brazil.
Univ Mississippi, Dept Math, POB 1848, University, MS 38677 USA.
2019 (English)In: Journal of Fixed Point Theory and Applications, ISSN 1661-7738, E-ISSN 1661-7746, Vol. 21, no 3, article id 77Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
SPRINGER BASEL AG , 2019. Vol. 21, no 3, article id 77
National Category
Geometry
Identifiers
URN: urn:nbn:se:uu:diva-390376DOI: 10.1007/s11784-019-0714-yISI: 000475753600001OAI: oai:DiVA.org:uu-390376DiVA, id: diva2:1341794
Funder
EU, European Research Council, StG-239781Knut and Alice Wallenberg FoundationAvailable from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-12Bibliographically approved

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