Low-regularity Seiberg-Witten moduli spaces on manifolds with boundary

2021/07/08 by Piotr Suwara, Suwara, Piotr
Mathematics · Physics and Astronomy · #57R58 (Secondary) #58J32 (Primary) 57K41 #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2107.03977

openalex publication_date 2021/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a compact spinc manifold X with boundary b₁(∂ X)=0, we consider moduli spaces of solutions to the Seiberg-Witten equations in a generalized double Coulomb slice in L²₁ (i.e., W^1,2) Sobolev regularity. We prove they are Hilbert manifolds, prove denseness and "semi-infinite-dimensionality" properties of the restriction to ∂ X, and establish a gluing theorem. To achieve these, we prove a general regularity theorem and a strong unique continuation principle for Dirac operators, and smoothness of a restriction map to configurations of higher regularity on the interior, all of which are of independent interest.

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