A line bundle is a special case of vector bundle with dim(F)=1. The structure group is necessarily abelian. This is true for complex and real vector spaces.

Ex: a wave function in quantum mechanics is a section of a line bundle. Base space is tex2html_wrap76 , tex2html_wrap77 , so tex2html_wrap78 is normally trivial. For a magnetic monopole, remove of a point from M gives twisting of the bundle.


source
psfile jl@crush.caltech.edu index
holomorphic_line_bundle
canonical_line_bundle
splitting_principle