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On higher scissors congruence

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arxiv 2210.08082 v3 pith:R2D33XQM submitted 2022-10-14 math.AT math.KT

Cary Malkiewich This is my paper · ORCID
classification math.ATmath.KT
keywords highercongruencescissorsspectrumgroupshomotopyproblemresult
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abstract

We solve the higher version of Hilbert's Third Problem for one-dimensional geometries, and in higher dimensions we reduce the problem to a computation in group homology. Our central result concerns the scissors congruence $K$-theory spectrum of Zakharevich, whose homotopy groups are the correct higher version of the classical scissors congruence groups. We prove that this spectrum is a Thom spectrum, whose base space is the homotopy orbit space of a Tits complex. The relevant computations quickly follow from this more foundational result.

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Cited by 1 Pith paper

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  1. 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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