Smoothly non-isotopic Lagrangian disk fillings of Legendrian knots

Geometriae Dedicata (2020)Cite this article

Abstract

In this paper, we construct the first families of distinct Lagrangian ribbon disks in the standard symplectic 4-ball which have the same boundary Legendrian knots, and are not smoothly isotopic or have non-homeomorphic exteriors.

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Acknowledgements

The authors would like to thank John Etnyre and Honghao Gao for useful conversations. We are also grateful to the referee(s) for valuable suggestions. Part of this work was carried out while the first author was visiting University of Tsukuba and he would like to thank for their hospitality. The first author was partially supported by Grant No. 11871332 of the National Natural Science Foundation of China. The second author was partially supported by JSPS KAKENHI Grant Number 17K14180.

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Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China

    Youlin Li

  2. Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8571, Japan

    Motoo Tange

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  1. Youlin Li
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  2. Motoo Tange
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Correspondence to Youlin Li.

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Li, Y., Tange, M. Smoothly non-isotopic Lagrangian disk fillings of Legendrian knots. Geom Dedicata (2020). https://doi.org/10.1007/s10711-020-00575-x

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Keywords

  • Legendrian knots
  • Lagrangian disks
  • Isotopy.

Mathematics Subject Classification

  • 57R17 (57K33, 57K40)