Sphere bundles and spin (Ex)
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- For , determine the number of distinct -bundles over .
- Let be the complex plane bundle with Euler number . Explain how to obtain the sphere-bundle via surgery on .
- For , let be a nullhomotopic embedding. For spin, show that there is more than one possible effect for a surgery on this embedding.
Now suppose is simply connected. For not spin, show that the effect of a surgery on this embedding is uniquely determined (difficult!).