The asymptotic dimension of quotients by finite groups

Let $X$ be a proper metric space and let $F$ be a finite group acting on $X$ by isometries. We show that the asymptotic dimension of $F\backslash X$ is the same as the asymptotic dimension of $X$.Comment: 7 page

Coarse embeddings into products of trees

We give a short and elementary proof of the fact that every metric space of finite asymptotic dimension can be embedded into a finite product of trees.Comment: 4 pages; mistake in the proof of Lemma 6 fixed and some typos corrected; to appear in Kyoto Journal of Mathematic

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

We prove that for every finitely generated subgroup of a virtually connected Lie group which admits a finite dimensional model for the classifying space for proper actions the assembly map in algebraic K-theory is split injective. We also prove a similar statement for algebraic L-theory, which in particular implies the integral Novikov conjecture for such groups.Comment: 13 page

Algebraic K-theory of stable ∞\infty-categories via binary complexes

We adapt Grayson's model of higher algebraic $K$-theory using binary acyclic complexes to the setting of stable $\infty$-categories. As an application, we prove that the $K$-theory of stable $\infty$-categories preserves infinite products.Comment: 20 pages; accepted for publication by the Journal of Topolog

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

We generalize the proof of the Farrell-Jones conjecture for CAT(0)-groups to a larger class of groups in particular also containing all hyperbolic groups. This way we give a unified proof for both classes of groups.Comment: 17 page

K1K_1-groups via binary complexes of fixed length

We modify Grayson's model of $K_1$ of an exact category to give a presentation whose generators are binary acyclic complexes of length at most $k$ for any given $k \ge 2$. As a corollary, we obtain another, very short proof of the identification of Nenashev's and Grayson's presentations.Comment: 10 pages, minor changes following a referee report, to appear in HH