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.
ISBN: | 9781470431068 |
Publication date: | 30th November 2016 |
Author: | Adam Clay, Dale Rolfsen |
Publisher: | American Mathematical Society |
Format: | Hardback |
Pagination: | 154 pages |
Series: | Graduate Studies in Mathematics |
Genres: |
Geometry Topology |