5 papers
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…