Ordered Groups and Topology

Description

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 w.  Read more... Abstract: 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. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology.  Read more... Content: 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.