Networking Seifert surgeries on knots
 Author/Creator
 Deruelle, Arnaud, 1974
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2011.
 Physical description
 vii, 130 p. : ill ; 26 cm.
 Series
 Memoirs of the American Mathematical Society ; no. 1021.
Access
Available online

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QA3 .A57 NO.1021

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QA3 .A57 NO.1021
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 127130).
 Publisher's Summary
 The authors propose a new approach in studying Dehn surgeries on knots 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 knot $K$ is a trivial knot 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 another knot admitting a Seifert surgery. Edges of the network correspond to such twistings. A path in the network from one Seifert surgery to another 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 known Seifert surgeries to those on torus knots, 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 knots which cannot be embedded in a genus two Heegaard surface of $S^3$.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2011
 Responsibility
 Arnaud Deruelle, Katura Miyazaki, Kimihiko Motegi.
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1021
 Note
 "May 2012, volume 217, number 1021 (third of 4 numbers)."
 ISBN
 9780821853337 (alk. paper)
 0821853333 (alk. paper)