Real Places and Surface Bundles

2010/05/20 by Sinick, Jonah
#57M10 #57M27 #57M50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1005.3856

Abstract

Our results complement D. Calegari's result that there are no hyperbolic once-punctured torus bundles over S¹ with trace field having real place. We exhibit several infinite families of pairs (-χ, p) such that there exist hyperbolic surface bundles with over S¹ with fiber having p punctures and Euler characteristic χ with trace field of having a real place. This supports our conjecture that there exist such examples for each pair (-χ, p) with finitely many known exceptions.

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