Tight contact structures on hyperbolic homology 3-spheres

Mahan Mj, Balarka Sen

Published 2024-04-23Version 1

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. We also introduce a notion of geometric limits of contact structures compatible with geometric limits of hyperbolic manifolds. We study the behavior of the tight contact structures we construct under geometric limits.