Abstract
The cohomology algebra of the space H∗ (X) defines neither cohomology modules of the loop space H∗ (ΩX) nor cohomologies of the free loop space H∗ (ΛX). But by the author’s minimality theorem, there exists a structure of A(∞)-algebra (H∗ (X), {mi}) on H∗ (X), which determines H∗ (ΩX). Here will be shown that the same A(∞)-algebra (H∗(X), {mi}) determines also cohomology modules H∗ (ΛX).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 177, Algebra, 2020.
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Kadeishvili, T. A(∞)-Algebra Structure in the Cohomology and Cohomologies of a Free Loop Space. J Math Sci 275, 735–743 (2023). https://doi.org/10.1007/s10958-023-06715-4
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DOI: https://doi.org/10.1007/s10958-023-06715-4