Braid foliations in low-dimensional topology
著者
書誌事項
Braid foliations in low-dimensional topology
(Graduate studies in mathematics, v. 185)
American Mathematical Society, c2017
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注記
Includes bibliographical references (p. 281-285) and index
内容説明・目次
内容説明
This book is a self-contained introduction to braid foliation techniques, which is a theory developed to study knots, links and surfaces in general 3-manifolds and more specifically in contact 3-manifolds. With style and content accessible to beginning students interested in geometric topology, each chapter centers around a key theorem or theorems. The particular braid foliation techniques needed to prove these theorems are introduced in parallel, so that the reader has an immediate "take-home" for the techniques involved.
The reader will learn that braid foliations provide a flexible toolbox capable of proving classical results such as Markov's theorem for closed braids and the transverse Markov theorem for transverse links, as well as recent results such as the generalized Jones conjecture for closed braids and the Legendrian grid number conjecture for Legendrian links. Connections are also made between the Dehornoy ordering of the braid groups and braid foliations on surfaces.
All of this is accomplished with techniques for which only mild prerequisites are required, such as an introductory knowledge of knot theory and differential geometry. The visual flavor of the arguments contained in the book is supported by over 200 figures.
目次
Links and closed braids
Braid foliations and Markov's theorem
Exchange moves and Jones' conjecture
Transverse links and Bennequin's inequality
The transverse Markov theorem and simplicity
Botany of braids and transverse knots
Flypes and transverse nonsimplicity
Arc presentations of links and braid foliations
Braid foliations and Legendrian links
Braid foliations and braid groups
Open book foliations
Braid foliations and convex surface theory
Bibliography
Index.
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