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About this product
- DescriptionThe authors propose a new approach in studying Dehn surgeries on kts in the $3$-sphere $S^3$ yielding Seifert fiber spaces. The basic idea is finding relationships among such surgeries. To describe relationships and get a global picture of Seifert surgeries, they introduce seiferters and the Seifert Surgery Network, a $1$-dimensional complex whose vertices correspond to Seifert surgeries. A seiferter for a Seifert surgery on a kt $K$ is a trivial kt in $S^3$ disjoint from $K$ that becomes a fiber in the resulting Seifert fiber space. Twisting $K$ along its seiferter or an annulus cobounded by a pair of its seiferters yields ather kt admitting a Seifert surgery. Edges of the network correspond to such twistings. A path in the network from one Seifert surgery to ather explains how the former Seifert surgery is obtained from the latter after a sequence of twistings along seiferters and/or annuli cobounded by pairs of seiferters. The authors find explicit paths from various kwn Seifert surgeries to those on torus kts, the most basic Seifert surgeries. The authors classify seiferters and obtain some fundamental results on the structure of the Seifert Surgery Network. From the networking viewpoint, they find an infinite family of Seifert surgeries on hyperbolic kts which cant be embedded in a genus two Heegaard surface of $S^3$.
- Author(s)Arnaud Deruelle,Katura Miyazaki,Kimihiko Motegi
- PublisherAmerican Mathematical Society
- Date of Publication01/05/2012
- SubjectScience & Mathematics: Textbooks & Study Guides
- Series TitleMemoirs of the American Mathematical Society
- Series Part/Volume Number217, 1021
- Place of PublicationProvidence
- Country of PublicationUnited States
- ImprintAmerican Mathematical Society
- Weight369 g
- Width178 mm
- Height254 mm
- Edition StatementNew ed.
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