Homology, Homotopy and Applications

Volume 14 (2012)

Number 1

Scissors congruence as $K$-theory

Pages: 181 – 202

DOI: http://dx.doi.org/10.4310/HHA.2012.v14.n1.a9

Author

Inna Zakharevich (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Abstract

Scissors congruence groups have traditionally been expressed algebraically in terms of group homology. We give an alternate construction of these groups by producing them as the 0-level in the algebraic $K$-theory of a Waldhausen category.

Keywords

scissors congruence, K-theory, Waldhausen category

2010 Mathematics Subject Classification

13D15, 18D05, 18F25, 19Dxx

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