Scissors congruence of the line and the regulator

TL;DR

This paper constructs explicit generators for higher scissors congruence K-theory of the line and derives generators for the homology of interval exchange transformations, utilizing an extended regulator map.

Contribution

It provides explicit generators for higher scissors congruence K-theory of the line and the homology of interval exchange transformations, advancing understanding in geometric and algebraic structures.

Findings

Explicit generators for higher scissors congruence K-theory of the line.

Explicit generating set for the homology of interval exchange transformations.

Use of an extended regulator (trace) map in the proof.

Abstract

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.