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SFT COMPUTATIONS AND INTERSECTION THEORY IN HIGHER-DIMENSIONAL CONTACT MANIFOLDS

Part of: Symplectic geometry, contact geometry

Published online by Cambridge University Press:  25 January 2021

Agustin Moreno Open the ORCID record for Agustin Moreno [Opens in a new window]
Agustin Moreno*
Affiliation:
Uppsala Universitet, Uppsala, Sweden
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Abstract

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I construct infinitely many nondiffeomorphic examples of $5$ -dimensional contact manifolds which are tight, admit no strong fillings and do not have Giroux torsion. I obtain obstruction results for symplectic cobordisms, for which I give a proof not relying on the polyfold abstract perturbation scheme for Symplectic Field Theory (SFT). These results are part of my PhD thesis [23], and are the first applications of higher-dimensional Siefring intersection theory for holomorphic curves and hypersurfaces, as outlined in [23, 24], as a prequel to [30].

Keywords

Contact TopologySymplectic GeometryHolomorphic CurvesSymplectic Field Theory

MSC classification

Primary: 53D42: Symplectic field theory; contact homology
Secondary: 53D10: Contact manifolds, general 53D35: Global theory of symplectic and contact manifolds
Type
Review Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 4 , July 2022 , pp. 1219 - 1270
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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