English

Loops of Legendrians in contact 3-manifolds

Symplectic Geometry 2018-10-09 v1

Abstract

We study homotopically non-trivial spheres of Legendrians in the standard contact R3 and S3. We prove that there is a homotopy injection of the contactomorphism group of S3 into some connected components of the space of Legendrians induced by the natural action. We also provide examples of loops of Legendrians that are non-trivial in the space of formal Legendrians, and thus non-trivial as loops of Legendrians, but which are trivial as loops of smooth embeddings for all the smooth knot types.

Keywords

Cite

@article{arxiv.1810.03194,
  title  = {Loops of Legendrians in contact 3-manifolds},
  author = {Eduardo Fernández and Javier Martínez-Aguinaga and Francisco Presas},
  journal= {arXiv preprint arXiv:1810.03194},
  year   = {2018}
}

Comments

10 pages, 1 figure