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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
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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 |