A couple of real hyperbolic disc bundles over surfaces

Sasha Anan'in; Philipy V. Chiovetto

doi:10.4171/ggd/585

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arXiv · 1609.02206

A couple of real hyperbolic disc bundles over surfaces

Sasha Anan'in·Philipy V. Chiovetto

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Abstract

Applying the techniques developed in [AGG], we construct new real hyperbolic manifolds whose underlying topology is that of a disc bundle over a closed orientable surface. By the Gromov-Lawson-Thurston conjecture [GLT], such bundles $M\to S$ should satisfy the inequality $|eM/χS|\leqslant1$, where $eM$ stands for the Euler number of the bundle and $χS$, for the Euler characteristic of the surface. In this paper, we construct new examples that provide a maximal value of $|eM/χS|=\frac35$ among all known examples. The former maximum, belonging to Feng Luo [Luo], was $|eM/χS|=\frac12$.

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BibTeX RIS

Sasha Anan'in, Philipy V. Chiovetto. 2020-12-28. A couple of real hyperbolic disc bundles over surfaces. https://doi.org/10.4171/ggd%2F585

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