arXiv subjects

Christoph Winges

Publications and source records attributed to Christoph Winges.

22 records · Page 2Linked to original sources

arXiv2016

On the Farrell-Jones Conjecture for Waldhausen's $A$-theory

We prove the Farrell-Jones Conjecture for (non-connective) $A$-theory with coefficients and finite wreath products for hyperbolic groups, CAT(0)-groups, cocompact lattices in almost connected Lie groups and fundamental groups of manifolds of dimension less or equal to three. Moreover, we prove inheritance properties such as passing to subgroups, colimits of direct systems of groups, finite direct products and finite free products. These results hold also for Whitehead spectra and spectra of stable pseudo-isotopies in the topological, piecewise linear and smooth category.

math.GT↗

arXiv2016

The A-theoretic Farrell-Jones Conjecture for virtually solvable 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.

math.KT↗

arXiv2016

On the Farrell-Jones Conjecture for algebraic K-theory of spaces: the Farrell-Hsiang method

We prove the Farrell-Jones Conjecture for algebraic K-theory of spaces for virtually poly-Z-groups. For this, we transfer the 'Farrell-Hsiang method' from the linear case to categories of equivariant, controlled retractive spaces.

math.KT↗

arXiv2014

On the transfer reducibility of certain Farrell-Hsiang groups

We show how the existing proof of the Farrell-Jones Conjecture for virtually poly-$\mathbb{Z}$-groups can be improved to rely only on the usual inheritance properties in combination with transfer reducibility as a sufficient criterion for the validity of the conjecture.

math.GT↗