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 and their homology
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…