Hyperbolic Manifolds, Harmonic Forms, and Seiberg-Witten Invariants

2001/11/26 by Claude LeBrun, LeBrun, Claude · 3 citations
Mathematics · #53C21 #57R57 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #math.GT #msc:53C21 #msc:57R57

paper · pdf · doi:10.48550/arxiv.math/0111265

22 pages, LaTeX2e

arxiv created 2001/11/26 · openalex publication_date 2001/11/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Counting hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants
• A hyperbolic 4-orbifold with underlying space ℙ²
• Monopole Floer homology and the spectral geometry of three-manifolds

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