On the doubled tetrus

Mathematics – Geometric Topology

Scientific paper

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17 pages, 6 figures. Extensively rewritten with clarity in mind

Scientific paper

The tetrus is a sort of big brother to the tripus, W.P. Thurston's example of a compact hyperbolic 3-manifold with totally geodesic boundary. We describe a sixfold cover of the double of the tetrus, itself a double, which fibers over the circle with fiber a closed surface of genus 19. We also record arithmeticity of the doubles and certain twisted doubles of the tripus and tetrus, and point out some consequences regarding families of covers.

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