Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424941 | Advances in Mathematics | 2017 | 43 Pages |
Abstract
In this paper we introduce the notion of an assembler, which formally encodes “cutting and pasting” data. An assembler has an associated K-theory spectrum, in which Ï0 is the free abelian group of objects of the assembler modulo the cutting and pasting relations, and in which the higher homotopy groups encode further geometric invariants. The goal of this paper is to prove structural theorems about this K-theory spectrum, including analogs of Quillen's localization and dévissage theorems. We demonstrate the uses of these theorems by analyzing the assembler associated to the Grothendieck ring of varieties and the assembler associated to scissors congruence groups of polytopes.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Inna Zakharevich,