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DLIN
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rank 2 complex vector over $S^2\times S^2$

How could people classify all rank $2$ complex vector over $S^2\times S^2$ up to isomorphic? And could give a rank 2 complex bundle which can bot be split as a sum of two line bundles.

Thanks a lot.

DLIN
  • 1.9k
  • 1
  • 10
  • 19