Analytic K-homology draws together ideas from algebraic topology, functional analysis and
geometry. It is a tool-a means of conveying information among these three subjects-and it …

A good deal of research in C∗-algebra K-theory in recent years has been devoted to the
Baum-Connes conjecture [3], which proposes a formula for the K-theory of group C∗ …

The Atiyah-Singer index theorem is one of the most powerful tools for relating geometry,
analysis, and topology. In its original form, however, it applies only to compact manifolds …

We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the
algebraic K-and L-theory of integral group rings and to the Baum–Connes Conjecture on the …

Algebraic K-theory encodes important invariants for several mathematical disciplines,
spanning from geometric topology and functional analysis to number theory and algebraic …

There is the general principle to consider a classical invariant of a closed Riemannian
manifold M and to define its analog for the universal covering M taking the action of the …

arXiv:math/0402405v1 [math.KT] 25 Feb 2004 Page 1 arXiv:math/0402405v1 [math.KT] 25
Feb 2004 The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory Wolfgang …

Index theory studies the solutions to differential equations on geometric spaces, their
relation to the underlying geometry and topology, and applications to physics. If the space of …

A concise introduction to the techniques used to prove the Baum-Connes conjecture. The
Baum-Connes conjecture predicts that the K-homology of the reduced C^*-algebra of a …

Let X be an orientable closed compact Riemannian manifold with fundamental group Γ. Let
X be a Galois Γ-covering and r: X→ BΓ a classifying map for X. The signature package for …