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.
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}
}