Open books supporting overtwisted contact structures and the Stallings twist

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概要

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• We study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called “twisting loop”. We show that the existence of a twisting loop on the fiber surface of an open book is equivalent up to positive stabilization to the existence of an overtwisted disk in the contact manifold supported by the open book. We also show a criterion for overtwistedness using a certain arc properly embedded in the fiber surface, which is an extension of Goodmans one.

• 社団法人 日本数学会の論文
• 2007-07-01

著者

• Yamamoto Ryosuke

  Osaka City University Advanced Mathematical Institute

関連論文

• Open books supporting overtwisted contact structures and the Stallings twist

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