Scissors congruence of the line and the regulator

Ezekiel Lemann

Scissors congruence of the line and the regulator

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arxiv 2505.08676 v2 pith:GAEIJ6NZ submitted 2025-05-13 math.KT

Ezekiel Lemann This is my paper · ORCID

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keywords congruenceexplicitlineregulatorscissorsbohmannconstructderive

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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.

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The Dennis Trace for Assembler K-Theory
math.AT 2026-07 conditional novelty 7.5 of 10

A Dennis trace from assembler K-theory to Hochschild homology of scissors correspondences refines the regulator, making group homology a trace invariant.

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