The paper develops a generalized Hodge theory in which sequences of overdetermined boundary-value systems satisfying a weaker order-reduction property are lifted to genuine cochain complexes whose cohomology is explicitly described.
A version of scale calculus and the associated Fredholm theory
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abstract
This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and the existence of a constant rank theorem for such maps. It does so by extending the notion of linear Fredholm maps from [HWZ14] and [Weh12] to a setting where the Nash-Moser inverse function theorem can be applied and which also encompasses the necessary examples such as the reparametrisation action and (nonlinear) elliptic partial differential operators.
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math.DG 1years
2025 1verdicts
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Hodge Theory for Linearized Boundary-Value Problems on General Geometric Structures
The paper develops a generalized Hodge theory in which sequences of overdetermined boundary-value systems satisfying a weaker order-reduction property are lifted to genuine cochain complexes whose cohomology is explicitly described.