TL;DR
This paper investigates the gradient flow of a modified Rabinowitz action functional on negative line bundles, linking it to periodic orbits on the base, and highlights the absence of holomorphic spheres in such bundles.
Contribution
It introduces a novel analysis of gradient flows on negative line bundles and their relation to periodic orbits, expanding understanding in symplectic topology.
Findings
Gradient flow equations relate to periodic orbits on the base.
Very negative line bundles typically lack holomorphic spheres.
The study connects Floer theory with geometric properties of line bundles.
Abstract
In this article we study the gradient flow equation of a variant of the Rabinowitz action functional on very negative line bundles and relate it to periodic orbits on the base of this bundle. On very negative line bundles there are generically no holomorphic spheres.
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