Ordered Groups and Topology

by Adam Clay, Dale Rolfsen

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.

154 pages, Hardcover

Published November 16, 2016

About the author

Adam Clay's most recent book is Circle Back (Milkweed Editions, 2024). His poems have appeared in Tin House, jubilat, Boston Review, Ploughshares, Denver Quarterly, Iowa Review, New Orleans Review, and elsewhere. He teaches at Louisiana State University and edits AUTOCORRECT, a journal of poetry and poetics.