Ideal Perturbation Lemma

TL;DR

The paper introduces the Ideal Perturbation Lemma, a refined framework for understanding perturbation problems through strong chain homotopy equivalences, unifying classical and new results.

Contribution

It presents the Ideal Perturbation Lemma and the concept of strong chain homotopy equivalence, advancing the theoretical understanding of perturbation problems.

Findings

Established the Ideal Perturbation Lemma

Defined strong chain homotopy equivalence

Unified classical and new perturbation results

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 prove an Ideal Perturbation Lemma and show how both new and classical results follow from this ideal statement.