18 citations · 135 across the 39 of their papers we have counts for
49 papers
Double Steinberg coinvariants for special linear groups
Tatiana Abdelnaim, David Chan, Alexander Kupers +2
For a field we study the coinvariants for the -action on the double Steinberg module and show they have a rich algebraic structure: for $n =…
The Morita classes are nonzero
Alexander Kupers, Jeremy Miller, Peter Patzt
We prove that all Morita classes are nonzero using a novel description of the Hopf algebra structure on Steinberg homology. We prove anal…
Framed configuration spaces and exotic spheres
Manuel Krannich, Alexander Kupers, Fadi Mezher
We determine when an exotic sphere of dimension can be detected through the homotopy type of its truncated Disc-presheaf. The latter records the diagram of…
Pontryagin-Weiss classes and a rational decomposition of spaces of homeomorphisms
Manuel Krannich, Alexander Kupers
We construct a rational homotopy pullback decomposition for variants of the classifying space of the group of homeomorphisms for a large class of manifolds. This has various applic…
Infinity-operadic foundations for embedding calculus
Manuel Krannich, Alexander Kupers
Motivated by applications to spaces of embeddings and automorphisms of manifolds, we consider a tower of -categories of truncated right-modules over a unital -opera…
Scissors automorphism groups I: Homological stability and K-theory
Alexander Kupers, Ezekiel Lemann, Cary Malkiewich +2
In any category with a reasonable notion of cover, each object has a group of scissors automorphisms. We prove that under mild conditions, the homology of this group is independent…
The bounded cohomology of transformation groups of Euclidean spaces and discs
Francesco Fournier-Facio, Nicolas Monod, Sam Nariman +1
We prove that the groups of orientation-preserving homeomorphisms and diffeomorphisms of are boundedly acyclic, in all regularities. This is the first full computati…
A note on homotopy and pseudoisotopy of diffeomorphisms of -manifolds
Manuel Krannich, Alexander Kupers
This note serves to record examples of diffeomorphisms of closed smooth -manifolds that are homotopic but not pseudoisotopic to the identity, and to explain why there are no…
Mapping class groups of exotic tori and actions by
Mauricio Bustamante, Manuel Krannich, Alexander Kupers +1
We determine for which exotic tori of dimension the homomorphism from the group of isotopy classes of orientation-preserving diffeomorphisms of …
The first two k-invariants of Top/O
Alexander Kupers
We show that the first two -invariants of Top/O vanish and give some applications.
Two remarks on spaces of maps between operads of little cubes
Geoffroy Horel, Manuel Krannich, Alexander Kupers
We record two facts on spaces of derived maps between the operads of little -cubes. Firstly, these mapping spaces are equivalent to the mapping spaces between the non-unit…
Stability of concordance embeddings
Thomas Goodwillie, Manuel Krannich, Alexander Kupers
We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.
The Disc-structure space
Manuel Krannich, Alexander Kupers
We study the Disc-structure space of a compact smooth manifold . Informally speaking, this space measures the difference between , together with it…
Mapping class groups of manifolds with boundary are of finite type
Alexander Kupers
In this note we prove that the mapping class group of a compact topological manifold with boundary is of finite type, under assumptions on its dimension and connectivity.
Improved homological stability for certain general linear groups
Alexander Kupers, Jeremy Miller, Peter Patzt
We prove that the general linear groups of the integers, Gaussian integers, and Eisenstein integers satisfy homological stability of slope 1 when using -coefficien…
On the Torelli Lie algebra
Alexander Kupers, Oscar Randal-Williams
We prove two theorems about the Malcev Lie algebra associated to the Torelli group of a surface of genus : stably, it is Koszul and the kernel of the Johnson homomorphism consis…
On Torelli groups and Dehn twists of smooth 4-manifolds
Manuel Krannich, Alexander Kupers
This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of . Secondly, we give an alter…
Finiteness properties of automorphism spaces of manifolds with finite fundamental group
Mauricio Bustamante, Manuel Krannich, Alexander Kupers
Given a closed smooth manifold of even dimension with finite fundamental group, we show that the classifying space of the diffeomorphism group of …
Embedding calculus for surfaces
Manuel Krannich, Alexander Kupers
We prove convergence of Goodwillie-Weiss' embedding calculus for spaces of embeddings into a manifold of dimension at most two, so in particular for diffeomorphisms between surface…
There is no topological Fulton-MacPherson compactification
Alexander Kupers
In this note we prove that the Fulton-MacPherson compactification of configuration spaces of smooth manifolds can not be extended to topological manifolds in a natural manner, usin…
An -bundle over with nontrivial -genus
Manuel Krannich, Alexander Kupers, Oscar Randal-Williams
We explain the existence of a smooth -bundle over whose total space has nontrivial -genus. Combined with an argument going back to Hitchin, this answers a ques…
On diffeomorphisms of even-dimensional discs
Alexander Kupers, Oscar Randal-Williams
We determine for completely in degrees , far beyond the pseudoisotopy stable range. Furthermore, above th…
Framings of
Alexander Kupers, Oscar Randal-Williams
We compute the set of framings of , up to homotopy and diffeomorphism relative to the boundary.
On the generalized Bykovskii presentation of Steinberg modules
Alexander Kupers, Jeremy Miller, Peter Patzt +1
We study presentations of the virtual dualizing modules of special linear groups of number rings, the Steinberg modules. Bykovskii gave a presentation for the Steinberg modules of…