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Networking Seifert surgeries on knots by Arnaud Deruelle, Katura Miyazaki, Kimihiko Motegi is a nonfiction available to read on EtoBox.

What is Networking Seifert surgeries on knots about?

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. F

Who reads Networking Seifert surgeries on knots?

Author

Arnaud Deruelle, Katura Miyazaki, Kimihiko Motegi

Publisher

American Mathematical Society

Published

2012

Language

EN

ISBN

9780821853337

Category

nonfiction

Subjects

Mathematics, Stem