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Oct
17
revised Triviality of a differentiable sphere bundle
added 18 characters in body; deleted 5 characters in body
Oct
17
awarded  Scholar
Oct
17
comment Triviality of a differentiable sphere bundle
Thanks for your explicit answer! I only wanted the existence of a section for $n=2$ in order to simplify a proof but I know almost nothing about this theory, so I decided to pose my question here. Now, I have corrected the original statement.
Oct
17
accepted Triviality of a differentiable sphere bundle
Oct
17
awarded  Supporter
Oct
17
comment Triviality of a differentiable sphere bundle
Thanks for pointing that out. I was confused since I only wanted the result for $n=2$ and the actual statement and what I wrote coincide for $n=2$. Now, I have rewritten the original statement.
Oct
17
revised Triviality of a differentiable sphere bundle
corrected statement
Oct
17
comment Triviality of a differentiable sphere bundle
I am definitely not an expert on fiber bundles, so I messed everything up when I stated the theorem I wanted. As M. Murray says, I want existence of section for total space of dimension $3$, base of dimension $2$ and fiber a circle. Thanks for pointing out the counterexample so all is clearer now!!
Oct
16
awarded  Editor
Oct
16
revised Triviality of a differentiable sphere bundle
added 1 characters in body
Oct
16
revised Triviality of a differentiable sphere bundle
deleted 22 characters in body
Oct
16
answered Triviality of a differentiable sphere bundle
Oct
16
comment Triviality of a differentiable sphere bundle
Ok, I was mistaken. What they prove is that it admits a global section. Note that the fibers are circles.
Oct
16
awarded  Student
Oct
16
asked Triviality of a differentiable sphere bundle