Chapter 15 - L2-Invariants of Regular Coverings of Compact Manifolds and CW-Complexes

Abstract

When we were asked to write this survey article for the Handbook of Geometry, we began to wonder who will read such an article. Well, certainly not someone who wants to fix his car. The possible readers couldbe (1) students or more advanced mathematicians who are looking for new problems, (2) people who are curious about this topic and want to get a first impression, (3) others who are interested in this topic already and want to invest some time to learn more about the techniques, (4) experts who want to see new developments and an extensive list of literature (with all their papers cited) or (5) people who want to read and absorb something new without big effort while watching a Star Trek episode or a soccer game. We hope that any of these groups can get something from this survey article. The appeal of the topic comes from its connections to rather different fields of mathematics like spectral theory of the Laplace operator, questions about metrics with certain curvature properties on manifolds, isomorphism conjectures in algebraic K-theory and the Baum-Connes Conjecture, low-dimensional manifolds, group theory, index theory, intersection homology, representation theory of Lie groups and so on.