On Embedding Hamming Spheres with Applications to Positive Curvature

We consider isometric $\mathbb{Z}_{p}$-torus actions on closed, positively curved manifolds, obtaining a homotopy classification result. This allows us to strengthen on the improvement of the $3n/8$ half-maximal symmetry rank result of Fang-Rong and Ghazawneh given in Theorem B and Corollary C in the work of the author and Searle. Along the way, we generalize a sphere-embedding construction of Wilking from the binary case to arbitrary primes in Theorem C, which is a geometric construction of independent interest.