Infinitely Many Hyperbolic 3-manifolds Which Contain No Reebless Foliation
نویسندگان
چکیده
It has long been realized that the presence of a Reebless foliation in a compact 3-manifold M reveals useful topological information about M . By Novikov [No65], M is irreducible with infinite fundamental group. By Palmeira [Pa78], M has universal cover R. Building on work of Thurston and Gabai and Kazez [Ga98, GK98], Calegari [Ca] has shown that if M is also atoroidal, then π1(M) is Gromov negatively curved. Furthermore, Thurston has proposed an approach to demonstrating geometrization for such M . Many 3-manifolds contain Reebless foliations, and it has often been conjectured that all closed hyperbolic 3-manifolds do. (It is our impression that for many years Hatcher provided the sole voice of dissent.) In this paper, we give the first examples of closed hyperbolic 3-manifolds which contain no Reebless foliation.
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