Open books supporting overtwisted contact structures and Stallings twist

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dc.creatorYamamoto, Ryosuke
dc.date2006-08-15
dc.date2006-08-28
dc.date.accessioned2026-07-07T07:21:48Z
dc.date.available2026-07-07T07:21:48Z
dc.descriptionWe 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 Goodman's one.
dc.description11 pages, 12 figures
dc.identifierhttps://arxiv.org/abs/math/0608371
dc.identifierhttp://arxiv.org/abs/math/0608371
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115428
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject57M50, 57R17; 57M25
dc.titleOpen books supporting overtwisted contact structures and Stallings twist
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