2018/07/22 by Tsuyoshi Kato, Kato, Tsuyoshi, Hirofumi Sasahira +3
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 #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1807.08239
openalex publication_date 2018/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Anti-self-dual (ASD) connections for a compact smooth four manifold arise as critical values for the Yang-Mills action functional. Nahm transform is a nice correspondence between a vector bundle with ASD connections and a vector bundle with ASD connections over Picard torus associated to X. In this talk we propose a noncommutative geometric version of the Nahm transform that generalises the Connes-Yang-Mills action functional formulated using Dixmier trace.