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Irregularity and the period determinant for irregular singular connections on surfaces
Author(s) -
Hien M.
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710042
Subject(s) - mathematics , connection (principal bundle) , period (music) , pairing , isomorphism (crystallography) , sheaf , pure mathematics , product (mathematics) , topology (electrical circuits) , surface (topology) , geometry , combinatorics , physics , chemistry , superconductivity , quantum mechanics , acoustics , crystal structure , crystallography
Abstract 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)