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Abstract
We explain the essence of perturbation problems. The key to understanding is the structure of chain homotopy equivalence – the standard one must be replaced by a finer notion which we call a strong chain homotopy equivalence.
We formulate an Ideal Perturbation Lemma and show how both new and classical (including the Basic Perturbation Lemma) results follow from this ideal statement.
ACKNOWLEDGMENTS
I would like to express my thanks to Jim Stasheff and Johannes Huebschmann for reading the manuscript and many useful comments, and apologize to the latter for not implementing all his suggestions. Also the suggestions of the referee were extremely helpful. Supported by the grant GA ČR 201/99/0675.