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 ...

Let M be an oriented 3-dimensional manifold. By a result of Giroux [6] there is a one-to-one correspondence between open book decompositions of M (up to stabilization) and contact structures on M (up to isotopy). In [5] Etnyre and Ozbagci consider three invariants associated with a fixed contact structure defined in terms of all open book decompositions supporting it: (1) the support genus, whi...

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Reading is a hobby to open the knowledge windows. Besides, it can provide the inspiration and spirit to face this life. By this way, concomitant with the technology development, many companies serve the e-book or book in soft file. The system of this book of course will be much easier. No worry to forget bringing the database and xml technologies 4th international xml database symposium xsym 20...

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