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How can I express the 2nd Hirzebruch surface, $F_{2}$ in terms of $SO(3)$.

Is it true that $F_{2}$ is the total space of a bundle with fibre SO(3) over $\mathbb{R}_{+}$?

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It's Hirzebruch, the r comes before the z :) –  t.b. Jun 16 '11 at 2:22
Can you define $F_2$? –  Alon Amit Jun 16 '11 at 4:30
it is the 2nd Hirzebruch surface see map.him.uni-bonn.de/index.php/Hirzebruch_surfaces –  J Verma Jun 16 '11 at 4:42
$SO(3)\times[a,b]$ has boundary and Hirzebruch surfaces don't. –  Grigory M Jun 16 '11 at 8:02
No, since this total space is not compact –  Grigory M Jun 16 '11 at 19:31

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