English

On Transverse Knots and Branched Covers

Geometric Topology 2007-12-11 v1 Symplectic Geometry

Abstract

We study contact manifolds that arise as cyclic branched covers of transverse knots in the standard contact 3-sphere. We discuss properties of these contact manifolds and describe them in terms of open books and contact surgeries. In many cases we show that such branched covers are contactomorphic for smoothly isotopic transverse knots with the same self-linking number. These pairs of knots include most of the non-transversely simple knots of Birman-Menasco and Ng-Ozsvath-Thurston.

Keywords

Cite

@article{arxiv.0712.1557,
  title  = {On Transverse Knots and Branched Covers},
  author = {Shelly Harvey and Keiko Kawamuro and Olga Plamenevskaya},
  journal= {arXiv preprint arXiv:0712.1557},
  year   = {2007}
}

Comments

29 pages, 25 figures

R2 v1 2026-06-21T09:52:33.557Z