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On Embedding Hamming Spheres with Applications to Positive Curvature
Abstract
We consider isometric ℤp-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.
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BibTeX
@misc{abdullah2026embedding,
title = {{On Embedding Hamming Spheres with Applications to Positive Curvature}},
author = {Muhammad Abdullah},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00483},
eprint = {2609.00483},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00483},
}
RIS
TY - UNPB
TI - On Embedding Hamming Spheres with Applications to Positive Curvature
AU - Muhammad Abdullah
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00483
UR - https://arxiv.org/abs/2609.00483
AB - We consider isometric 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.
ER -