3 papers
math.AT2026
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…
math.KT2025
Scissors congruence of the line and the regulator
Ezekiel Lemann
We construct explicit generators for the higher scissors congruence K-theory of the line. We use this to derive an explicit generating set for the homology of the group of interval…
math.KT2024
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…