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# Homology, Homotopy and Applications

## Volume 13 (2011)

### Number 2

### On the algebraic $K$-theory of the coordinate axes over the integers

Pages: 103 – 111

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n2.a7

#### Authors

#### Abstract

We show that the relative algebraic $K$-theory group $K_{2i}(\mathbb{Z}[x, y]/(xy), (x, y))$ is free abelian of rank 1 and that $K_{2i+1}(\mathbb{Z}[x, y]/(xy), (x, y))$ is finite of order $(i!)^2$. We also find the group structure of $K_{2i+1}(\mathbb{Z}[x, y]/(xy), (x, y))$ in low degrees.

#### Keywords

algebraic $K$-theory, equivariant homotopy, topological cyclic homology

#### 2010 Mathematics Subject Classification

19D55, 55Q91

Published 25 January 2012