Bibliothèque de L'IMIST/CNRST

Includes bibliographical references and index.

CW complexes and homotopy -- Cellular homology -- Fundamental group and tietze transformations -- Some techniques in homotopy theory -- Elementary geometric topology -- The borel construction and Bass-Serre theory -- Topological finiteness properties and dimension of groups -- Homological finiteness properties of groups -- Finiteness properties of some important groups -- Locally finite CW complexes and proper homotopy -- Locally finite homology -- Cohomology of CW complexes -- Cohomology of groups and ends of covering spaces -- Filtered ends of pairs of groups -- Poincaré duality in manifolds and groups -- The fundamental group at infinity -- Higher homotopy theory of groups -- Three essays.

"Topological Methods in Group Theory is about the interplay between algebraic topology and the theory of infinite discrete groups. The author has kept three kinds of readers in mind: graduate students who have had an introductory course in algebraic topology and who need a bridge from common knowledge to the current research literature in geometric, combinatorial and homological group theory; group theorists who would like to know more about the topological side of their subject but who have been too long away from topology; and manifold topologists, both high- and low-dimensional, since the book contains much basic material on proper homotopy and locally finite homology not easily found elsewhere." "Illustrative examples treated in some detail include: Bass-Serre Theory, Coxeter groups, Thompson groups, Whitehead's contractible 3-manifold, Davis's exotic contractible manifolds in dimensions greater than three, the Bestvina-Brady Theorem, and the Bieri-Neumann-Strebel invariant. The book also includes a highly geometrical treatment of Poincare duality (via cells and dual cells) to bring out the topological meaning of Poincare duality groups."--Jacket.