2006/09/15 by Marco Hien, Hien, Marco
Mathematics · #14F40 #32S40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0609439
openalex publication_date 2006/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define homology groups for flat irregular singular connections on surfaces and a pairing between these and the de Rham cohomology of the connection, generalizing work of S. Bloch and H. Enault in dimension one. Assuming a conjecture of C. Sabbah (known to be true if the rank of the vector bundle is at most 5), we prove perfectness of the pairing. We comment on certain new phenomena appearing in dimension two.