Daniel Kasprowski

On the K-theory of groups with finite decomposition complexity

It is proved that the assembly map in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups

The A‐theoretic Farrell–Jones conjecture for virtually solvable groups

\Gamma

On the K-theory of linear groups

with finite quotient finite decomposition complexity (a strengthening of finite decomposition complexity introduced by Guentner, Tesser and Yu) that admit a finite dimensional model for

The asymptotic dimension of quotients by finite groups

\underbar E\Gamma

Regular finite decomposition complexity

and have an upper bound on the order of their finite subgroups. In particular this applies to finitely generated linear groups over fields with characteristic zero with a finite dimensional model for

The Farrell–Jones conjecture for hyperbolic and CAT(0)-groups revisited

\underbar E\Gamma

Stable classification of 4-manifolds with 3-manifold fundamental groups

.

On the K–theory of subgroups of virtually connected Lie groups

We prove the A-theoretic Farrell-Jones Conjecture for virtually solvable groups. As a corollary, we obtain that the conjecture holds for S-arithmetic groups and lattices in almost connected Lie groups.

Shrinking of toroidal decomposition spaces

We prove that for a finitely generated linear group G over a field of positive characteristic the family of quotients by finite subgroups has finite asymptotic dimension. We use this to show that the K-theoretic assembly map for the family of finite subgroups is split injective for every finitely generated linear group G over a commutative ring with unit under the assumption that G admits a finite-dimensional model for the classifying space for the family of finite subgroups. Furthermore, we prove that this is the case if and only if an upper bound on the rank of the solvable subgroups of G exists.

Equivariant coarse homotopy theory and coarse algebraic

Let