An infinite family of hyperbolic 3-manifolds without tight projectively Anosov flows

Abstract

In this paper we find the first infinite family of hyperbolic 3-manifolds which admit tight contact structures but do not have any tight projectively Anosov flow. These manifolds are obtained as rational surgeries on the figure eight knot.

arXiv commentThe computation on page 11 contains a mistake. The values of the $d_3$ invariants of the tight contact structures obtained by positive surgery coefficients are wrong. In fact, the hyperbolic manifolds considered in the paper admit Taut foliations and hence pairs of tight structures (positive and negative) that are homotopic. The author thanks Ying Hu for pointing out the mistake