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Exact Lagrangian caps and non-uniruled Lagrangian submanifolds

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Abstract

We make the elementary observation that the Lagrangian submanifolds of C n, n≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov–Eliashberg algebra is acyclic.

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Authors and Affiliations

  1. Département de Mathématiques, Université Paris-Sud, Bat. 425, FR-91405, Orsay, France

    Georgios Dimitroglou Rizell

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  1. Georgios Dimitroglou Rizell
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Correspondence to Georgios Dimitroglou Rizell.

Additional information

This work was partially supported by the ERC starting grant of Frédéric Bourgeois StG-239781-ContactMath.

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Dimitroglou Rizell, G. Exact Lagrangian caps and non-uniruled Lagrangian submanifolds. Ark Mat 53, 37–64 (2015). https://doi.org/10.1007/s11512-014-0202-y

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  • DOI: https://doi.org/10.1007/s11512-014-0202-y

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