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