Geodesic
Steenrod problem and some graded Stanley–Reisner rings
Takeda, Masahiro1
1 Faculty of Mathematics, Kyushu University, Fukuoka, Japan
Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1725-1738

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

“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. 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. We give a necessary and sufficient condition that a graded Stanley–Reisner ring is realizable when there is no pair of generators x,y such that |x| = |y| = 2n and xy≠0.

DOI : 10.2140/agt.2024.24.1725
Keywords: Steenrod problem, Stanley–Reisner ring, homotopy colimit, Steenrod algebra

Takeda, Masahiro 1

1 Faculty of Mathematics, Kyushu University, Fukuoka, Japan 
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Takeda, Masahiro. Steenrod problem and some graded Stanley–Reisner rings. Algebraic and Geometric Topology, Tome 24 (2024) no. 3, pp. 1725-1738. doi: 10.2140/agt.2024.24.1725

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