Braid foliations in low-dimensional topology

著者

• LaFountain, Douglas J.
• Menasco, William W.

書誌事項

Braid foliations in low-dimensional topology

Douglas J. LaFountain, William W. Menasco

（Graduate studies in mathematics, v. 185）

American Mathematical Society, c2017

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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詳細情報

• NII書誌ID(NCID): BB24779653
• ISBN:
  • 9781470436605
• LCCN: 2017016585
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xi, 289 p.
• 大きさ: 27 cm
• 分類:
  • LCC : QA612.23
  • DC23 : 514/.72
• 件名:
  • LCSH : Braid theory -- Textbooks
  • LCSH : Foliations (Mathematics) -- Textbooks
  • LCSH : Topology -- Textbooks
• 親書誌ID:
  • BA20542214