Ordered groups and topology
著者
書誌事項
Ordered groups and topology
（Graduate studies in mathematics, v. 176）
American Mathematical Society, c2016
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注記
Includes bibliographical references (p. 147-152) and index
内容説明・目次
内容説明
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.
目次
Orderable groups and their algebraic properties
Hoelder'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
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