English

Legendrians with vanishing Shelukhin-Chekanov-Hofer metric

Symplectic Geometry 2024-09-10 v2

Abstract

We show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin-Chekanov-Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang.

Keywords

Cite

@article{arxiv.2301.07575,
  title  = {Legendrians with vanishing Shelukhin-Chekanov-Hofer metric},
  author = {Lukas Nakamura},
  journal= {arXiv preprint arXiv:2301.07575},
  year   = {2024}
}

Comments

3 pages; minor revision, added a brief comparison to a similar result by Cant; accepted for publication in Arkiv f\"or Matematik