The converse of isovariant Borsuk-Ulam results for some abelian groups

Abstract

The isovariant Borsuk-Ulam theorem provides nonexistence results on isovariant maps between representations. In this paper we shall deal with the existence problem of isovariant maps as a converse to the isovariant Borsuk-Ulam theorem, and show that the converse holds for representations of an abelian $p$-group or a cyclic groups of order $p^{n}q^{m}$ or $pqr$, where $p,q,r$ are distinct primes.