Kaledin classes and formality criteria
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909183148818432 |
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| author | Emprin, Coline |
| author_facet | Emprin, Coline |
| contents | We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded algebras over operads or properads, possibly colored in groupoids. The present treatment generalizes the previous obstruction classes in two directions: outside characteristic zero and including a wider range of algebraic structures. This enables us to establish novel formality criteria, including formality descent with torsion coefficients, formality in families, intrinsic formality, and criteria in terms of chain-level lifts of homology automorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kaledin classes and formality criteria Emprin, Coline Algebraic Topology Algebraic Geometry Quantum Algebra 18D50, 18G55, 17B60 16W25, 13D10 We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded algebras over operads or properads, possibly colored in groupoids. The present treatment generalizes the previous obstruction classes in two directions: outside characteristic zero and including a wider range of algebraic structures. This enables us to establish novel formality criteria, including formality descent with torsion coefficients, formality in families, intrinsic formality, and criteria in terms of chain-level lifts of homology automorphism. |
| title | Kaledin classes and formality criteria |
| topic | Algebraic Topology Algebraic Geometry Quantum Algebra 18D50, 18G55, 17B60 16W25, 13D10 |
| url | https://arxiv.org/abs/2404.17529 |