Hardcover ISBN:  9781470436605 
Product Code:  GSM/185 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470442682 
Product Code:  GSM/185.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470436605 
eBook: ISBN:  9781470442682 
Product Code:  GSM/185.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Hardcover ISBN:  9781470436605 
Product Code:  GSM/185 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470442682 
Product Code:  GSM/185.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470436605 
eBook ISBN:  9781470442682 
Product Code:  GSM/185.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 

Book DetailsGraduate Studies in MathematicsVolume: 185; 2017; 304 ppMSC: Primary 57; 20
This book is a selfcontained introduction to braid foliation techniques, which is a theory developed to study knots, links and surfaces in general 3manifolds and more specifically in contact 3manifolds. 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 “takehome” 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.
ReadershipGraduate students and researchers interested in geometry and topology.

Table of Contents

Chapters

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


Additional Material

Reviews

This research monograph is a highly readable and pleasant introduction to the toolkits that the authors call braid foliation techniques, a small but relatively underdeveloped corner of lowdimensional topology and geometry. It is written at a level that will be accessible to graduate students and researchers and is carefully structured and filled with useful examples.
J.S. Birman, Mathematical Reviews 
The AMS once more presents the mathematical community with a strong text geared to getting graduate students and other relative beginners into the game. The present book is thorough and wellstructured, leads the reader pretty deeply into the indicated parts of knot and linktheory and lowdimensional topology and does so effectively and (as far as I can tell) rather painlessly...All in all, the book looks like a hit.
Michael Berg, MAA Reviews


RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
This book is a selfcontained introduction to braid foliation techniques, which is a theory developed to study knots, links and surfaces in general 3manifolds and more specifically in contact 3manifolds. 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 “takehome” 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.
Graduate students and researchers interested in geometry and topology.

Chapters

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

This research monograph is a highly readable and pleasant introduction to the toolkits that the authors call braid foliation techniques, a small but relatively underdeveloped corner of lowdimensional topology and geometry. It is written at a level that will be accessible to graduate students and researchers and is carefully structured and filled with useful examples.
J.S. Birman, Mathematical Reviews 
The AMS once more presents the mathematical community with a strong text geared to getting graduate students and other relative beginners into the game. The present book is thorough and wellstructured, leads the reader pretty deeply into the indicated parts of knot and linktheory and lowdimensional topology and does so effectively and (as far as I can tell) rather painlessly...All in all, the book looks like a hit.
Michael Berg, MAA Reviews