7 papers
On the surjectivity conjectures of Dupont and Monod
Alexander Kupers, Daniil Rudenko, Ismael Sierra
In this paper we apply our work on polylogarithmic cocycles representing the Borel classes to establish that the comparison map from bounded continuous cohomology to continuous coh…
Mixed Tate motives over number fields
Alexander Kupers, Daniil Rudenko, Ismael Sierra
This paper relates algebraic K-theory of fields to polylogarithms via general linear groups. We focus on the case of number fields and prove that the motivic realisation map from t…
The Goncharov Lie coalgebra of a field
Alexander Kupers, Daniil Rudenko, Ismael Sierra
This paper relates algebraic -theory of fields to polylogarithms via general linear groups. We introduce the Goncharov Lie coalgebra, defined in terms of the -homology…
Scissors automorphism groups II: Solomon-Tits theorems
Alexander Kupers, Ezekiel Lemann, Cary Malkiewich +2
The Solomon-Tits theorem says that the poset of proper non-trivial subspaces of a finite-dimensional vector space has realisation equivalent to a wedge of spheres. In this paper we…
Some remarks on -cobordisms between smooth 4-manifolds
Alexander Kupers, Mark Powell
It is not known whether the realisation part of the -cobordism theorem holds for smooth 4-manifolds, nor whether every pair of smoothly -cobordant 4-manifolds is also smoothl…
Manifolds and Disc-presheaves
Alexander Kupers
This essay explains an approach to the study of smooth manifolds which compares them to presheaves on a category of discs, also known as embedding calculus. We highlight recent wor…
A stable rank filtration on direct sum -theory
Jonathan Campbell, Alexander Kupers, Inna Zakharevich
In the literature, there are two standard rank filtrations on -theory: an ``unstable'' one which is traditionally defined through the homology of , and a ``stable'' one wh…