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Symplectic homology of complements of smooth divisors
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Univ Mississippi, Dept Math, University, MS USA.
2019 (English)In: Journal of Topology, ISSN 1753-8416, E-ISSN 1753-8424, Vol. 12, no 3, p. 967-1030Article in journal (Refereed) Published
Abstract [en]

If (X,omega) is a closed symplectic manifold, and sigma is a smooth symplectic submanifold Poincare dual to a positive multiple of omega, then X set minus sigma can be completed to a Liouville manifold (W,d lambda). Under monotonicity assumptions on X and on sigma, we construct a chain complex whose homology computes the symplectic homology of W. We show that the differential is given in terms of Morse contributions, Gromov-Witten invariants of X relative to sigma and Gromov-Witten invariants of sigma. We use a Morse-Bott model for symplectic homology. Our proof involves comparing Floer cylinders with punctures to pseudoholomorphic curves in the symplectization of the unit normal bundle to sigma.

Place, publisher, year, edition, pages
2019. Vol. 12, no 3, p. 967-1030
Keywords [en]
53D40 (primary), 53D45 (secondary)
National Category
Geometry
Identifiers
URN: urn:nbn:se:uu:diva-394970DOI: 10.1112/topo.12105ISI: 000486205600010OAI: oai:DiVA.org:uu-394970DiVA, id: diva2:1360160
Funder
EU, European Research CouncilEU, European Research CouncilKnut and Alice Wallenberg FoundationAvailable from: 2019-10-11 Created: 2019-10-11 Last updated: 2019-10-11Bibliographically approved

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