Real Places and Surface Bundles

Abstract

Our results complement D. Calegari's result that there are no hyperbolic once-punctured torus bundles over $S^1$ with trace field having real place. We exhibit several infinite families of pairs $(-\chi ,p)$ such that there exist hyperbolic surface bundles with over $S^1$ with fiber having $p$ punctures and Euler characteristic $\chi$ with trace field of having a real place. This supports our conjecture that there exist such examples for each pair $(-\chi ,p)$ with finitely many known exceptions.

13 pages, 5 figures

References in corpus (1)

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle