Effective hyperbolization and length bounds for Heegaard splittings

2024/08/13 by Feller, Peter, Sisto, Alessandro, Viaggi, Gabriele
#57K20 #57K32 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2408.06998

Abstract

We consider 3-manifolds given as Heegaard splittings M=H^-∪_ΣH⁺ with the aim to describe the hyperbolic metric of M under topological conditions on the splitting guaranteeing that the manifold is hyperbolic. In particular, given a suitable "sufficiently incompressible" curve γ⊂Σ, we show (without appealing to Geometrization) that M is hyperbolic and we compute the length of γ in terms of the projection coefficients of the disk sets, up to a uniform multiplicative error.

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