SIGMA 22 (2026), 032, 38 pages      arXiv:2510.20945      https://doi.org/10.3842/SIGMA.2026.032
Contribution to the Special Issue on Geometry and Dynamics in memory of Will Merry

The Linearized Floer Equation in a Chart

Urs Frauenfelder ^a and Joa Weber ^b
a) Universität Augsburg, Germany
^b) Unicamp, Campinas, Brazil

Received October 31, 2025, in final form March 11, 2026; Published online April 01, 2026

Abstract
In this article, we are considering the Hessian of the area functional in a non-Darboux chart. This does not seem to have been considered before and leads to an interesting new mathematical structure which we introduce in this article and refer to as almost extendable weak Hessian field. Our main result is a Fredholm theorem for Robbin-Salamon operatorsassociated to non-continuous Hessians which we prove by taking advantage of this new structure.

Key words: Fredholm; Robbin-Salamon operators; Floer theory; para-Darboux.

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