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arXiv · 2207.10884

Steenrod problem and some graded Stanley-Reisner rings

Masahiro Takeda
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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.

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Masahiro Takeda. 2022-07-22. Steenrod problem and some graded Stanley-Reisner rings. https://doi.org/10.2140/agt.2024.24.1725

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