An almost classification of compact Lie groups with Borsuk-Ulam properties
We say that a compact Lie group G has the Borsuk-Ulam property in the weak sense if for every orthogonal representation V of G and every G- equivariant map f: S(V)\(\to S(V)\), \(V^ 0=\{0\}\), of the unit sphere we have deg \(f\neq 0\). We say that G has the Borsuk-Ulam property in the strong sense if for any two orthogonal representations V, W of G with dim W\(=\dim V\) and \(W^ 0=V^ 0=\{0\}\) and every G-equivariant map f: S(V)\(\to S(W)\) of the unit sphere, we have deg \(f\neq 0\). In this paper a complete classification, up to isomorphism, of groups with the weak Borsuk-Ulam property is given. A classification of groups with the strong Borsuk-Ulam property does not cover nonabelian p-groups with all elements of order p. In fact, we deal with a more general definition admitting a nonempty fixed point set of G on the sphere S(V).
scientific article; zbMATH DE number 4122862