Isovariant maps from free -manifolds to representation spheres

The isovariant version of Borsuk–Ulam type theorems has been studied by Wasserman and the first author. In this paper, first we consider the relation between the existence of C n -isovariant maps from free C n -manifolds to representation spheres and Borsuk–Ulam type inequalities for their dimensions. Our main result classifies the C n -isovariant maps by C n -isovariant homotopy types when a Borsuk–Ulam type inequality holds. For proving it, we use the multidegree of a C n -equivariant map developed by the first author.