\(A_\infty\)-structures and the \({\mathcal D}\) functor (Q2710718)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(A_\infty\)-structures and the \({\mathcal D}\) functor |
scientific article |
Statements
27 December 2001
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\(A_\infty\)-structure
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Berikashvili's \({\mathcal D}\) functor
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twisting cochain
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twisting family
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Massey product
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polynomial algebras
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\(A_\infty\)-structures and the \({\mathcal D}\) functor (English)
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Let \(X\) be a chain complex, and let \({\mathcal D}_\infty(X)\) be the set of equivalence classes of \(A_\infty\)-structures on \(X\). In this paper, the functor \({\mathcal D}_\infty\) is related to \textit{N. A. Berikashvili}'s \({\mathcal D}\)-functor [``On differentials of a spectral sequence'', Tr. Tbilis. Mat. Inst. Razmadze 51 (1976; Zbl 0416.55010)], which is a set of equivalence classes of twisting cochains. In particular, both functors are filtered in similar ways by using Massey products. The results are applied to polynomial algebras over the field with two elements; there are complete computations for algebras with up to four generators, and partial computations for algebras with more than four generators.
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