A correction to a paper of H. King
In his paper [ibid. 37, 193-199 (1976; Zbl 0318.57037)], \textit{H. C. King} shows that a conjecture of Thom is false, if one can find a smooth compact connected n-dimensional submanifold N of \(S^ n\) such that \(NK_ 0({\mathbb{Z}}[\pi_ 1N])\neq 0\) and \(\tilde K_ 0({\mathbb{Z}}[\pi_ 1(\partial N\times S^ 1)])=0\). His candidate had \(\pi_ 1N={\mathbb{Z}}_ 2\oplus {\mathbb{Z}}_ 2\), \(\partial N=\partial_ 1N\cup^{.}\partial_ 2N\), \(\partial_ iN\) connected and \(\pi_ 1(\partial_ iN)={\mathbb{Z}}_ 2\), \(i=1,2\). Such a manifold doesn't exist, but one having the desired properties can be constructed.
homeomorphism class of a germ of a submanifold
homeomorphism type of a germ of an analytic map
scientific article; zbMATH DE number 4005156