Steenrod problem and some graded Stanley-Reisner rings
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910518878404608 |
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| author | Takeda, Masahiro |
| author_facet | Takeda, Masahiro |
| contents | ``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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10884 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Steenrod problem and some graded Stanley-Reisner rings Takeda, Masahiro Commutative Algebra Algebraic Topology 55N10, 55R35, 13F55 ``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. |
| title | Steenrod problem and some graded Stanley-Reisner rings |
| topic | Commutative Algebra Algebraic Topology 55N10, 55R35, 13F55 |
| url | https://arxiv.org/abs/2207.10884 |