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How can I express the second 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](http://en.wikipedia.org/wiki/Friedrich_Hirzebruch), the r comes before the z :)2011-06-16
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    Can you define $F_2$?2011-06-16
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    it is the 2nd Hirzebruch surface see http://www.map.him.uni-bonn.de/index.php/Hirzebruch_surfaces2011-06-16
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    $SO(3)\times[a,b]$ has boundary and Hirzebruch surfaces don't.2011-06-16
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    No, since this total space is not compact2011-06-16
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    (Maybe adding some background would help? How did you come to these hypotheses?)2011-06-16
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    x-posted (and answered there): http://mathoverflow.net/questions/67992/hirzebruch-surfaces2011-06-17

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