Volumes of hyperbolic Haken manifolds. I
The main result of this paper says that the volume of a closed hyperbolic 3-manifold \(M\) must exceed 0.34, provided it contains a non-separating surface whose complement is not a book of I-bundles. Using results from their previous work, the authors construct an open cover of the universal covering of \(M\) given by certain neighborhoods of the axis of hyperbolic elements of \(\pi_1M\). A very careful analysis reveals that this cover has combinatorial features which, under the assumption that \(\text{vol} (M)>0.34\) and that \(M\) contains a non-separating surface \(S\), imply that the complement of \(S\) must be a book of I-bundles.
scientific article; zbMATH DE number 703870
scientific article