Journal of the Ramanujan Mathematical Society

Volume 41, Issue 1, March 2026 pp. 75–104.

Tight contact structures on hyperbolic homology 3-spheres

Authors: Mahan Mj and Balarka Sen
Author institution:School of Mathematics, Tata Institute of Fundamental Research 1, Homi Bhabha Road, Mumbai 400 005, India.

Summary: 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.

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