A Borsuk-Ulam theorem for Heisenberg group actions

Abstract

Let G = $H_{2n+1}$ be a (2n + 1)-dimensional Heisenberg Lie group acts on M = $C^m$ — {0} and M' = $C^{m'}$ — {0} exponentially. By using Cohomological Index we proved the following theorem. If $f : M rightarrow M'$ is a G-equivariant map, then $mleq m'$.