Monopole Floer homology and SOLV geometry

Abstract

We study the monopole Floer homology of a SOLV rational homology sphere Y from the point of view of spectral theory. Applying ideas of Fourier analysis on solvable groups, we show that for suitable SOLV metrics on Y, small regular perturbations of the Seiberg-Witten equations do not admit irreducible solutions; in particular, this provides a geometric proof that Y is an L-space.

References in corpus (3)

• An Introduction to Geometric Topology
• Lectures on monopole Floer homology
• The Seiberg-Witten equations and the length spectrum of hyperbolic three-manifolds