On \(K_ 1\)-theory of the Euclidean space
It is shown that any \(n\) by \(n\) matrix of determinant 1, \(n\geq 3\), whose entries are continuous real functions of \(N=3\) variables, can be reduced to the identity matrix by addition operations (with continuous coefficients). In the case \(n=2\), this is not true. The case of \(N=1\) was done in a previous paper by a different method. The case of arbitrary \(N\) is finished by a different method in a paper to appear in Proc. Am. Math. Soc. The similar result for polynomial functions (n\(\geq 3)\) is due to A. Suslin.
\(K_ 1\) of ring of continuous functions of three variables
algebraic K- theory of rings of continuous functions
Stone-Čech compactification on the Euclidean space
scientific article; zbMATH DE number 3987533