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- W287768124 abstract "In this paper, we discuss Thurston’s inequalities for foliations on 3-manifolds ,w hich are closely related to Thurston-Bennequin’s inequalities for contact structures (on 3manifolds). They hold if the structures are convex in some sense. As the theory of foliations and contact topology have exhibited so many similarities, Eliashberg and Thurston [ETh] developed the theory of confoliations to clarify the reason as well as to unify two theories to a certain extent. The relation between the above inequalities is one of its main subjects. The main result of this paper is to show the violation of Thurston’s inequality for spinnable foliations (i.e., a foliation associated with an open book decomposition) under certain conditions on the monodromy (Theorem c, C), as well as the (non-)vanishing of the Euler class of the tangent bundle to those foliations (Theorem a, A, Proposition b, B). These results are stated in §2 and proved in §3. In §4, some application to the mapping class of the monodromy is given, by passing through the relative inequality from the absolute one. One of the key ideas in this paper is to introduce the notion of being (non-)skinny for the monodromy. This notion is described along the statements of the main results. In the rest of this section we review Thurston’s inequality and some relevant results concerning monodromy of spinnable foliations." @default.
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- W287768124 date "2005-01-01" @default.
- W287768124 modified "2023-09-26" @default.
- W287768124 title "On Thurston's inequality for spinnable foliations Dedicated to Professor Shigeyuki Morita on the occasion of his 60th birthday" @default.
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