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Mathematics > Geometric Topology
Title: Tight contact structures on hyperbolic homology 3-spheres
(Submitted on 23 Apr 2024)
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. 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.
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