Abstract
In the paper conditions are found under which the A∞-structure on the homology of a differential algebra degenerates. Examples of such algebras are given. In particular, it is shown that the A∞-algebra structure on the Milnor coalgebra degenerates, and that if the cohomology of a topological space is a polynomial algebra, then the A∞-algebra structure on it degenerates.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
J. D. Stashe., “Homotopy associativity of H-spaces,” Trans. Amer. Math. Soc., 108 (1963), no. 2, 275-312.
T. V. Kadeishvili, “On the theory of homology of fiber spaces,” Uspekhi Mat. Nauk [Russian Math. Surveys], 35 (1980), no. 3, 183-188.
V. A. Smirnov, “A∞-structures and the functor D,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSRIzv.] (to appear).
V. A. Smirnov, “On the cochain complex of topological spaces,” Mat. Sb. [Math. USSR-Sb.], 115 (1981), no. 1, 146-158.
J. F. Adams, “On the structure and applications of the Steenrod algebra,” Comm. Math. Helv., 32 (1958), 180-214.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Smirnov, V.A. A Degeneracy Criterion for A∞-Structures. Mathematical Notes 69, 827–832 (2001). https://doi.org/10.1023/A:1010238700642
Issue Date:
DOI: https://doi.org/10.1023/A:1010238700642