\n In his seminal 19 76 paper Bill Thurston\n observed that a closed leaf \\(S\\) of a f oliation has Euler\n characteristic equal\, up to sign\, to the Eul er class of the\n foliation evaluated on \\([S]\\)\, the homology c lass represented\n by \\(S\\). We give a converse for taut foliati ons: if the\n underlying manifold is hyperbolic and if the Euler cl ass of a\n taut foliation \\(F\\) evaluated on \\([S]\\) equals\, u p to sign\,\n the Euler characteristic of \\(S\\)\, then there exis ts another\n taut foliation \\(F'\\) such that \\(S\\) is homologou s to a union\n of leaves and such that the plane field of \\(F'\\) is homotopic\n to that of \\(F\\). In particular\, \\(F\\) and \\( F'\\) have the\n same Euler class.\n
\n\n In the same paper Thurston proved that taut foliations on\n closed hyperbolic three-manifolds have Euler class of norm at\n most one\, and conjectured that\, conversely\, any integral\n cohomology clas s with norm equal to one is the Euler class of\n a taut foliation. Work of Yazdi\, together with our main\n result\, give a negative answer to Thurston's conjecture.\n
\n\n This is j oint work with Mehdi Yazdi.\n
\n LOCATION:https://researchseminars.org/talk/GaTO/29/ END:VEVENT END:VCALENDAR