A fixed point approach to homological perturbation theory

Barnes, Donald W.; Lambe, Larry A.

doi:10.1090/S0002-9939-1991-1057939-0

A fixed point approach to homological perturbation theory
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by Donald W. Barnes and Larry A. Lambe PDF

Proc. Amer. Math. Soc. 112 (1991), 881-892 Request permission

Correction: Proc. Amer. Math. Soc. 129 (2001), 941-941.

Abstract:

We show that the problem addressed by classical homological perturbation theory can be reformulated as a fixed point problem leading to new insights into the nature of its solutions. We show, under mild conditions, that the solution is essentially unique.

References

The twisted Eilenberg-Zilber theorem

Differential and integral calculus

V. K. A. M. Gugenheim, On the chain-complex of a fibration, Illinois J. Math. 16 (1972), 398–414. MR 301736
V. K. A. M. Gugenheim and L. A. Lambe, Perturbation theory in differential homological algebra. I, Illinois J. Math. 33 (1989), no. 4, 566–582. MR 1007895
V. K. A. M. Gugenheim, L. A. Lambe, and J. D. Stasheff, Algebraic aspects of Chen’s twisting cochain, Illinois J. Math. 34 (1990), no. 2, 485–502. MR 1046572
V. K. A. M. Gugenheim, L. A. Lambe, and J. D. Stasheff, Perturbation theory in differential homological algebra. II, Illinois J. Math. 35 (1991), no. 3, 357–373. MR 1103672
P. J. Hilton and S. Wylie, Homology theory: An introduction to algebraic topology, Cambridge University Press, New York, 1960. MR 0115161
Johannes Huebschmann and Tornike Kadeishvili, Small models for chain algebras, Math. Z. 207 (1991), no. 2, 245–280. MR 1109665, DOI 10.1007/BF02571387
Larry A. Lambe, Resolutions via homological perturbation, J. Symbolic Comput. 12 (1991), no. 1, 71–87. MR 1124305, DOI 10.1016/S0747-7171(08)80140-X
Larry Lambe and Jim Stasheff, Applications of perturbation theory to iterated fibrations, Manuscripta Math. 58 (1987), no. 3, 363–376. MR 893160, DOI 10.1007/BF01165893

Homology des espaces fibrés

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