arXiv subjects

Ezekiel Lemann

Publications and source records attributed to Ezekiel Lemann.

3 recordsLinked to original sources

arXiv2026

Scissors automorphism groups II: Solomon-Tits theorems

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 prove a variant of this result for collections of geodesic subspaces of Euclidean, hyperbolic, or spherical geometry, assuming the collection is generated either by points or by hyperplanes. In the third paper of this series of papers, we will combine this with the homological stability theorems from the first paper to compute the homology of groups of scissors automorphisms in these geometries.

math.AT↗

arXiv2025

Scissors congruence of the line and the regulator

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 exchange transformations. Our proof makes use of an extended version of the regulator (trace) map of Bohmann, Gerhardt, Malkiewich, Merling, and Zahkarevich.

math.KT↗

arXiv2024

Scissors automorphism groups and their homology

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 of the object, and can be expressed in terms of the scissors congruence K-theory spectrum defined by Zakharevich. We therefore obtain both a group-theoretic interpretation of Zakharevich's higher scissors congruence K-theory, as well as a method to compute the homology of scissors automorphism groups. We apply this to various families of groups, such as interval exchange groups and Brin--Thompson groups, recovering results of Szymik--Wahl, Li, and Tanner, and obtaining new results as well.

math.KT↗