Daniel Juan-Pineda

The Farrell-Jones Isomorphism Conjecture for finite covolume hyperbolic actions and the algebraic -theory of Bianchi groups

We prove the Farrell-Jones Isomorphism Conjecture for groups acting properly discontinuously via isometries on (real) hyperbolic n-space IHIn with finite volume orbit space. We then apply this result to show that, for any Bianchi group F, Wh(F), Ko(Zr), and Ki(Zr) vanish for i < -1.

The lower algebraic K-theory of Fuchsian groups

Abstract. Let

A geometric approach to the lower algebraic K-theory of Fuchsian groups

\Gamma

On the ring structure of K∗ for discrete groups

be a cocompact Fuchsian group. We calculate the lower algebraic K-theory of the integral group ring

The K and L Theoretic Farrell-Jones Isomorphism Conjecture for Braid Groups

{\Bbb Z} \Gamma

Models for classifying spaces for \({\mathbb {Z}\rtimes \mathbb {Z}}\)

and find an explicit formula for

On the virtually cyclic dimension of mapping class groups of punctured spheres

{\rm K}_{i}({\Bbb Z}\Gamma),\,i \le 1

Topological rigidity of higher graph manifolds

, in terms of the lower K-groups of maximal finite cyclic subgroups of

Algebraic K-Theory of Mapping Class Groups

\Gamma

INVARIANTS ASSOCIATED TO THE PURE BRAID GROUP OF THE SPHERE

.