The volume of a hyperbolic 3-manifold with Betti number 2

The volume of a hyperbolic $3$-manifold with Betti number $2$
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by Marc Culler and Peter B. Shalen PDF

Proc. Amer. Math. Soc. 120 (1994), 1281-1288 Request permission

If $M$ is a closed orientable hyperbolic $3$-manifold with first Betti number $2$ then the volume of $M$ exceeds $0.34$.

References

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Marc Culler and Peter B. Shalen, Paradoxical decompositions, $2$-generator Kleinian groups, and volumes of hyperbolic $3$-manifolds, J. Amer. Math. Soc. 5 (1992), no. 2, 231–288. MR 1135928, DOI 10.1090/S0894-0347-1992-1135928-4

Hyperbolic volume and

homology

Volumes of hyperbolic Haken manifolds

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torsion and hyperbolic volume

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A lower bound for the volume of hyperbolic

manifolds

34