A NONCOMMUTATIVE BORSUK-ULAM THEOREM FOR NATSUME-OLSEN SPHERES

The odd theta-deformed spheres are C*-algebras that admit natural actions by finite cyclic groups, and if one of these actions is fixed, any equivariant homomorphism between two spheres of the same dimension induces a nontrivial map on odd K-theory. This result is an extended, noncommutative Borsuk-Ulam theorem in odd dimension, and just as in the topological case, this theorem has many ( almost) equivalent formulations for theta-deformed spheres of arbitrary dimension. We also present theorems on graded Banach algebras, motivated by algebraic Borsuk-Ulam results of A. Taghavi.