21 citations · 82 across the 17 of their papers we have counts for
17 papers
Homology manifolds and euclidean bundles
Fabian Hebestreit, Markus Land, Michael Weiss +1
We construct a Poincaré complex whose periodic total surgery obstruction vanishes but whose Spivak normal fibration does not admit a reduction to a stable euclidean bundle. This co…
Every spectrum is the K-theory of a stable -category
Maxime Ramzi, Vladimir Sosnilo, Christoph Winges
We prove that any spectrum is equivalent to the nonconnective K-theory of a stable -category. We use these results to construct a stable -category wit…
On the Farrell-Jones conjecture for localising invariants
Ulrich Bunke, Daniel Kasprowski, Christoph Winges
We show the Farrell-Jones conjecture with coefficients in left-exact -categories for finitely -amenable groups and, more generally, Dress-Farrell-Hsiang-Jones…
Controlled objects in left-exact -categories and the Novikov conjecture
Ulrich Bunke, Denis-Charles Cisinski, Daniel Kasprowski +1
We associate to every -bornological coarse space and every left-exact -category with -action a left-exact infinity-category of equivariant -controlled objects.…
Split injectivity of A-theoretic assembly maps
Ulrich Bunke, Daniel Kasprowski, Christoph Winges
We construct an equivariant coarse homology theory arising from the algebraic -theory of spherical group rings and use this theory to derive split injectivity results for associ…
Homotopy theory with marked additive categories
Ulrich Bunke, Alexander Engel, Daniel Kasprowski +1
We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories…
-groups via binary complexes of fixed length
Daniel Kasprowski, Bernhard Köck, Christoph Winges
We modify Grayson's model of of an exact category to give a presentation whose generators are binary acyclic complexes of length at most for any given . As a cor…
Transfers in coarse homology
Ulrich Bunke, Alexander Engel, Daniel Kasprowski +1
We enlarge the category of bornological coarse spaces by adding transfer morphisms and introduce the notion of an equivariant coarse homology theory with transfers. We then show th…
Injectivity results for coarse homology theories
Ulrich Bunke, Alexander Engel, Daniel Kasprowski +1
We show injectivity results for assembly maps using equivariant coarse homology theories with transfers. Our method is based on the descent principle and applies to a large class o…
Algebraic K-theory of stable -categories via binary complexes
Daniel Kasprowski, Christoph Winges
We adapt Grayson's model of higher algebraic -theory using binary acyclic complexes to the setting of stable -categories. As an application, we prove that the -theory…
Coarse homology theories and finite decomposition complexity
Ulrich Bunke, Alexander Engel, Daniel Kasprowski +1
Using the language of coarse homology theories, we provide an axiomatic account of vanishing results for the fibres of forget-control maps associated to spaces with equivariant fin…
Equivariant coarse homotopy theory and coarse algebraic -homology
Ulrich Bunke, Alexander Engel, Daniel Kasprowski +1
We study equivariant coarse homology theories through an axiomatic framework. To this end we introduce the category of equivariant bornological coarse spaces and construct the univ…
Shortening binary complexes and commutativity of -theory with infinite products
Daniel Kasprowski, Christoph Winges
We show that in Grayson's model of higher algebraic -theory using binary acyclic complexes, the complexes of length two suffice to generate the whole group. Moreover, we prove t…
The A-theoretic Farrell-Jones Conjecture for virtually solvable groups
Daniel Kasprowski, Mark Ullmann, Christian Wegner +1
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…
On the Farrell-Jones Conjecture for Waldhausen's -theory
Nils-Edvin Enkelmann, Wolfgang Lück, Malte Pieper +2
We prove the Farrell-Jones Conjecture for (non-connective) -theory with coefficients and finite wreath products for hyperbolic groups, CAT(0)-groups, cocompact lattices in almos…
On the Farrell-Jones Conjecture for algebraic K-theory of spaces: the Farrell-Hsiang method
Mark Ullmann, Christoph Winges
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 catego…
On the transfer reducibility of certain Farrell-Hsiang groups
Christoph Winges
We show how the existing proof of the Farrell-Jones Conjecture for virtually poly--groups can be improved to rely only on the usual inheritance properties in combinatio…