Compact Perturbations of Fredholm n-tuples
Razvan Gelca (University of Iowa)
TL;DR
This paper investigates whether Fredholm pairs of index 0 can be perturbed by compact operators to achieve an exact Koszul complex, providing a negative answer to this question.
Contribution
It demonstrates that such perturbations are not always possible, clarifying limitations in the perturbation theory of Fredholm pairs.
Findings
Negative result on perturbing Fredholm pairs to exact complexes
Clarifies limitations in Fredholm perturbation theory
Contributes to the understanding of Fredholm n-tuples
Abstract
The paper gives a negative answer to the question whether one can perturb a Fredholm pair of index 0 by compact operators to a pair with exact Koszul complex.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Advanced Topics in Algebra