Ergodic Theoretic Methods in Group Homology a Minicourse on L2betti Numbers in Group Theory

Islamic powers in secular countries have presented a challenge for states around the world, including Indonesia, home to the largest Muslim population as well as the third largest democracy in the world.

This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.

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.