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


Vigleik Angeltveit (Department of Mathematics, Australian National University, Acton, Australia)

Teena Gerhardt (Department of Mathematics, Michigan State University, East Lansing, Mich., U.S.A.)


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.


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

2010 Mathematics Subject Classification

19D55, 55Q91

Published 25 January 2012