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Connections and Curvings on Lifting Bundle Gerbes
Author(s) -
Gomi Kiyonori
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702004076
Subject(s) - bundle , connection (principal bundle) , principal bundle , normal bundle , frame bundle , mathematics , class (philosophy) , pure mathematics , topology (electrical circuits) , geometry , computer science , line bundle , vector bundle , combinatorics , materials science , artificial intelligence , composite material
A connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension are constructed. The construction is based on certain structures on the bundle, that is, connections and bundle splittings. The Deligne cohomology class of the lifting bundle gerbe with the connection and with the curving coincides with the obstruction class of the lifting problem with these structures.