Description
Book SynopsisDeals 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. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology.
Trade ReviewThe 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 ReviewsTable of Contents
- Orderable groups and their algebraic properties
- Hölder’s theorem, convex subgroups and dynamics
- Free groups, surface groups and covering spaces
- Knots
- Three-dimensional manifolds
- Foliations
- Left-orderings of the braid groups
- Groups of homeomorphisms
- Conradian left-orderings and local indicability
- Spaces of orderings
- Bibliography
