On the hit problem for the polynomial algebra and the algebraic transfer
Algebraic Topology
2025-09-19 v4
Abstract
This paper investigates Singer's conjecture by examining the cohit module for specific degrees and values of . Utilizing hit problem techniques, we extend previous work by Mothebe et al. and establish key dimensional results. Notably, for , we prove that the cohit module's dimension in certain degrees matches the order of a specific factor group. Our contributions include demonstrating that certain non-zero elements do not belong to the image of the Singer algebraic transfer. All results were verified using the OSCAR computer algebra system.
Keywords
Cite
@article{arxiv.2412.02494,
title = {On the hit problem for the polynomial algebra and the algebraic transfer},
author = {Dang Vo Phuc},
journal= {arXiv preprint arXiv:2412.02494},
year = {2025}
}
Comments
104 pages. Update the appendix with the complete admissible monomial basis of degree 26 in $P_6$ and some $\Sigma_6$-invariants of $QP^{\otimes 6}_{26}$ associated with certain weight vectors