Irregularity and the period determinant for irregular singular connections on surfaces

In [6], we constructed a period pairing for flat irregular singular conncetions on surfaces. We now extend these constructions to a perfect period pairing between the irregularity complex of the connection and the complex of relative rapid decay chains. As a consequence, the period determinant of the connection decomposes as a product of a topological period determinant on the open surface and a determinant coming from the irregularity of the connection. Additionally, we deduce a method to compute the irregularity sheaf up to local isomorphism in topological terms (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)