Hardcover ISBN:  9781470431068 
Product Code:  GSM/176 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470435622 
Product Code:  GSM/176.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470431068 
eBook: ISBN:  9781470435622 
Product Code:  GSM/176.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Hardcover ISBN:  9781470431068 
Product Code:  GSM/176 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470435622 
Product Code:  GSM/176.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470431068 
eBook ISBN:  9781470435622 
Product Code:  GSM/176.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: 176; 2016; 154 ppMSC: Primary 20; 57
This book deals with the connections between topology and ordered groups. It begins with a selfcontained introduction to orderable groups and from there explores the interactions between orderability and objects in lowdimensional topology, such as knot theory, braid groups, and 3manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimensionone foliations and HeegaardFloer homology. The use of topological methods in proving algebraic results is another feature of the book.
The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
ReadershipGraduate students and researchers interested in lowdimensional topology, 3manifolds, and knot theory.

Table of Contents

Chapters

Chapter 1. Orderable groups and their algebraic properties

Chapter 2. Hölder’s theorem, convex subgroups and dynamics

Chapter 3. Free groups, surface groups and covering spaces

Chapter 4. Knots

Chapter 5. Threedimensional manifolds

Chapter 6. Foliations

Chapter 7. Leftorderings of the braid groups

Chapter 8. Groups of homeomorphisms

Chapter 9. Conradian leftorderings and local indicability

Chapter 10. Spaces of orderings


Additional Material

Reviews

The book finds a good balance between being a resource for researchers and a graduate textbook.
Sebastian Wolfgang Hensel, Mathematical Reviews 
The diligent and disciplined reader of this thin (<150 pp) book will be rewarded by a lot more than knowledge of ordered groups.
Lee P. Neuwirth, Zentralblatt MATH 
Given the huge popularity enjoyed by low dimensional topology these days, and all for good reason, it should make a very positive impact. The book is easy to read and deals with very pretty mathematics.
Michael Berg, MAA Reviews


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This book deals with the connections between topology and ordered groups. It begins with a selfcontained introduction to orderable groups and from there explores the interactions between orderability and objects in lowdimensional topology, such as knot theory, braid groups, and 3manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimensionone foliations and HeegaardFloer homology. The use of topological methods in proving algebraic results is another feature of the book.
The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
Graduate students and researchers interested in lowdimensional topology, 3manifolds, and knot theory.

Chapters

Chapter 1. Orderable groups and their algebraic properties

Chapter 2. Hölder’s theorem, convex subgroups and dynamics

Chapter 3. Free groups, surface groups and covering spaces

Chapter 4. Knots

Chapter 5. Threedimensional manifolds

Chapter 6. Foliations

Chapter 7. Leftorderings of the braid groups

Chapter 8. Groups of homeomorphisms

Chapter 9. Conradian leftorderings and local indicability

Chapter 10. Spaces of orderings

The book finds a good balance between being a resource for researchers and a graduate textbook.
Sebastian Wolfgang Hensel, Mathematical Reviews 
The diligent and disciplined reader of this thin (<150 pp) book will be rewarded by a lot more than knowledge of ordered groups.
Lee P. Neuwirth, Zentralblatt MATH 
Given the huge popularity enjoyed by low dimensional topology these days, and all for good reason, it should make a very positive impact. The book is easy to read and deals with very pretty mathematics.
Michael Berg, MAA Reviews