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On Holomorphic Principal Bundles Over a Compact Riemann Surface Admitting a Flat Connection, II
Author(s) -
Azad Hassan,
Biswas Indranil
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002182
Subject(s) - mathematics , connection (principal bundle) , holomorphic function , vector bundle , compact riemann surface , principal bundle , riemann surface , pure mathematics , frame bundle , line bundle , normal bundle , surface (topology) , vector valued differential form , linear algebraic group , group (periodic table) , mathematical analysis , algebraic number , geometry , chemistry , organic chemistry
Holomorphic principal bundles over a compact Riemann surface X that admits a flat connection are considered. A holomorphic G ‐bundle over X , where G is a connected semisimple linear algebraic group over C , admits a flat connection if and only if the adjoint vector bundle admits one. More generally, for a complex reductive group G , the necessary and sufficient condition on a G ‐bundle to admit a flat connection is described. This simplifies the criterion obtained by the authors and given in Math. Ann. 322 (2002) 333–346. 2000 Mathematics Subject Classification 53C05, 32L05.