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