Tight contact structures on hyperbolic homology 3-spheres
Abstract
We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class of oriented plane distributions. As a corollary, we give a recipe to construct hyperbolic L-spaces admitting arbitrarily many distinct tight contact structures. We also introduce a notion of geometric limits of contact structures compatible with geometric limits of hyperbolic manifolds and study the behavior of the tight contact structures we construct under geometric limits.
Cite
@article{arxiv.2404.14698,
title = {Tight contact structures on hyperbolic homology 3-spheres},
author = {Mahan Mj and Balarka Sen},
journal= {arXiv preprint arXiv:2404.14698},
year = {2024}
}
Comments
v2. 36 pages, 6 figures. Substantially revised: Corrected hypothesis in the case of links (Section 4.1), improved result from surgery coefficients in (0, 1) to all positive surgeries (Section 4.2), added application to tight contact structures on hyperbolic L-spaces (Section 4.3). Additional references and minor improvements in exposition. 3 figures added [v1 was 28 pgs, 3 figs]