English

Steenrod problem and some graded Stanley-Reisner rings

Commutative Algebra 2024-07-10 v3 Algebraic Topology

Abstract

``What kind of ring can be represented as the singular cohomology ring of a space?'' is a classic problem in algebraic topology, posed by Steenrod. In this paper, we consider this problem when rings are the graded Stanley-Reisner rings, in other words the polynomial rings divided by an ideal generated by square-free monomials. Under some assumption, we give a necessary and sufficiently condition that a graded Stanley-Reisner ring is realizable.

Keywords

Cite

@article{arxiv.2207.10884,
  title  = {Steenrod problem and some graded Stanley-Reisner rings},
  author = {Masahiro Takeda},
  journal= {arXiv preprint arXiv:2207.10884},
  year   = {2024}
}
R2 v1 2026-06-25T01:08:16.285Z