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Linking of Lagrangian Tori and Embedding Obstructions in Symplectic 4-Manifolds
Harvard Univ, Dept Math, 1 Oxford St, Cambridge, MA 02138 USA.;Sch Math, Inst Adv Study, 1 Einstein Dr, Princeton, NJ 08540 USA..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Geometri and Physics.ORCID iD: 0000-0003-4765-4979
2022 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, Vol. 2022, no 8, p. 6347-6401, article id rnaa384Article in journal (Refereed) Published
Abstract [en]

We classify weakly exact, rational Lagrangian tori in T*T-2 - 0(T2) up to Hamiltonian isotopy. This result is related to the classification theory of closed 1-forms on T-n and also has applications to symplectic topology. As a 1st corollary, we strengthen a result due independently to Eliashberg-Polterovich and to Giroux describing Lagrangian tori in T*T-2 - 0(T2), which are homologous to the zero section. As a 2nd corollary, we exhibit pairs of disjoint totally real tori K-1, K-2 subset of T*T-2, each of which is isotopic through totally real tori to the zero section, but such that the union K-1 boolean OR K-2 is not even smoothly isotopic to a Lagrangian. In the 2nd part of the paper, we study linking of Lagrangian tori in (R-4, omega) and in rational symplectic 4-manifolds. We prove that the linking properties of such tori are determined by purely algebro-topological data, which can often be deduced from enumerative disk counts in the monotone case. We also use this result to describe certain Lagrangian embedding obstructions.

Place, publisher, year, edition, pages
Oxford University Press (OUP) Oxford University Press, 2022. Vol. 2022, no 8, p. 6347-6401, article id rnaa384
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Geometry
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URN: urn:nbn:se:uu:diva-477829DOI: 10.1093/imrn/rnaa384ISI: 000755463900001OAI: oai:DiVA.org:uu-477829DiVA, id: diva2:1673520
Funder
Knut and Alice Wallenberg Foundation, KAW 2016.0198Available from: 2022-06-21 Created: 2022-06-21 Last updated: 2024-12-03Bibliographically approved

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Dimitroglou Rizell, Georgios

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