Originally published in 1989, this is an advanced text and research
monograph on groups acting on low-dimensional topological spaces,
and for the most part the viewpoint is algebraic. Much of the book
occurs at the one-dimensional level, where the topology becomes
graph theory. Two-dimensional topics include the characterization
of Poincare duality groups and accessibility of almost finitely
presented groups. The main three-dimensional topics are the
equivariant loop and sphere theorems. The prerequisites grow as the
book progresses up the dimensions. A familiarity with group theory
is sufficient background for at least the first third of the book,
while the later chapters occasionally state without proof and then
apply various facts which require knowledge of homological algebra
and algebraic topology. This book is essential reading for anyone
contemplating working in the subject.
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