Why Can Some Line Bundles Have Nonzero Sections While Others Cannot?

[duranduran]

Hey guys,
I am confused about the concept of sections of vector bundles. Mobius band is nontrivial line bundle over circle so we can not find any nonzero section from circle to mobius strip. However a plane which is twisted once is a trivial line bundle over line. That means there is a nonzero section for that bundle. How is it possible?

 

[mathwonk]

because the missing point of that twisted plane is the point where the section would have been zero.

 

[lavinia]

Hey guys,
I am confused about the concept of sections of vector bundles. Mobius band is nontrivial line bundle over circle so we can not find any nonzero section from circle to mobius strip. However a plane which is twisted once is a trivial line bundle over line. That means there is a nonzero section for that bundle. How is it possible?

Try constructing a non-zero section