Contact Structures of Closed 3-manifolds Fibred by the Circle

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概要

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• Consider the total space of a circle bundle over a closed orientable surface. In this paper we obtain a necessary and sufficient condition for this manifold to admit a contact structure transverse to the fibers of the circle bundle in terms of the genus of the surface and the Euler number of the bundle, which gives us a Milnor-Wood type inequality in a version of contact structures. There is a difference between the condition obtained by us and the one to admit such a contact structure with the invariance by the free action of the circle along the fibers.

• 明治大学の論文

著者

• 坪井 俊

  Graduate Scool Of Mathematical Sciences University Of Tokyo

• 佐藤 篤之

  Department of Mathematics School of Science and Technology, Meiji University

• 佐藤 篤之

  Department Of Mathematics School Of Science And Technology Meiji University

• 坪井 俊

  Graduate School of Mathematical Sciences University of Tokyo

関連論文

• Contact Structures of Closed 3-manifolds Fibred by the Circle
• A Remark on Plane Fields of Closed 3-manifolds Fibred by the Circle
• Notes on Complete Affine Flows without Closed Orbits on 3-Manifolds

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