2017/05/24 by Francesco Lin, Lin, Francesco
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1705.08817
openalex publication_date 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We refine some classical estimates in Seiberg-Witten theory, and discuss an application to the spectral geometry of three-manifolds. In particular, we show that on a rational homology three-sphere Y, for any Riemannian metric the first eigenvalue of the laplacian on coexact one-forms is bounded above explicitly in terms of the Ricci curvature, provided that Y is not an L-space (in the sense of Floer homology). The latter is a purely topological condition, and holds in a variety of examples. Performing the analogous refinement in the case of manifolds with b1>0, we obtain a gauge-theoretic proof of an inequality of Brock and Dunfield relating the Thurston and L2 norms of hyperbolic three-manifolds, first proved using minimal surfaces.