G-monopole invariants on some connected sums of 4-manifolds

2014/06/17 by Chanyoung Sung, Sung, Chanyoung
Mathematics · #57M60 #57R57 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M60 #msc:57R57

paper · pdf · doi:10.48550/arxiv.1406.4236

arXiv admin note: substantial text overlap with arXiv:1108.3875

arxiv created 2014/06/17 · openalex publication_date 2014/06/17 · arxiv updated 2014/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On a smooth closed oriented 4-manifold M with a smooth action of a finite group G on a Spin^c structure, G-monopole invariant is defined by "counting" G-invariant solutions of Seiberg-Witten equations for any G-invariant Riemannian metric on M. We compute G-monopole invariants on some G-manifolds. For example, the connected sum of k copies of a 4-manifold with nontrivial mod 2 Seiberg-Witten invariant has nonzero \Bbb Z_k-monopole invariant mod 2, where the \Bbb Z_k-action is given by cyclic permutations of k summands.

Citations

• Completion of the Proof of the Geometrization Conjecture
• Finite group actions and G-monopole classes on smooth 4-manifolds

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