Fredholm notions in scale calculus and Hamiltonian Floer theory
Symplectic Geometry
2025-09-12 v4
Abstract
We give an equivalent definition of the Fredholm property for linear operators on scale Banach spaces and introduce a (nonlinear) scale Fredholm property with respect to a splitting of the domain. The latter implies the Fredholm property introduced by Hofer-Wysocki-Zehnder in terms of contraction germs, but is easier to check in practice and holds in applications to holomorphic curve moduli spaces. We demonstrate this at the example of trajectory breaking in Hamiltonian Floer theory.
Keywords
Cite
@article{arxiv.1209.4040,
title = {Fredholm notions in scale calculus and Hamiltonian Floer theory},
author = {Katrin Wehrheim},
journal= {arXiv preprint arXiv:1209.4040},
year = {2025}
}
Comments
v4:The notion of "weakly regularizing" (in Def.4.3) was strengthened to fix a gap in the proof of the main theorem (Thm.4.5)