Hyperbolic Manifolds, Harmonic Forms, and Seiberg-Witten Invariants
Claude LeBrun
TL;DR
This paper investigates the behavior of harmonic forms on hyperbolic 4-manifolds and derives new estimates that lead to vanishing theorems for Seiberg-Witten invariants, advancing understanding in differential geometry.
Contribution
It introduces new estimates for harmonic 2-forms on hyperbolic 4-manifolds and applies them to prove vanishing results for Seiberg-Witten invariants.
Findings
Derived estimates for self-dual harmonic 2-forms.
Proved a vanishing theorem for Seiberg-Witten invariants on hyperbolic 4-manifolds.
Established connections between harmonic forms and topological invariants.
Abstract
New estimates are derived concerning the behavior of self-dual hamonic 2-forms on a compact Riemannian 4-manifold with non-trivial Seiberg-Witten invariants. Applications include a vanishing theorem for certain Seiberg-Witten invariants on compact 4-manifolds of constant negative sectional curvature.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds