Ordered Groups and Topology
About this Title
Adam Clay, University of Manitoba, Winnipeg, MB, Canada and Dale Rolfsen, University of British Columbia, Vancouver, BC, Canada
Publication: Graduate Studies in Mathematics
Publication Year: 2016; Volume 176
ISBNs: 978-1-4704-3106-8 (print); 978-1-4704-3562-2 (online)
MathSciNet review: MR3560661
MSC: Primary 57-02; Secondary 20F34, 20F36, 20F60, 57M07, 57M50
This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer 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 low-dimensional topology, 3-manifolds, and knot theory.
Table of Contents
- 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. Three-dimensional manifolds
- Chapter 6. Foliations
- Chapter 7. Left-orderings of the braid groups
- Chapter 8. Groups of homeomorphisms
- Chapter 9. Conradian left-orderings and local indicability
- Chapter 10. Spaces of orderings