most recent 30 from http://mathoverflow.net 2013-05-25T04:17:36Z http://mathoverflow.net/feeds/user/24094 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/126826/manifold-with-nonzero-pontryagin-number Yingfei Gu 2013-04-08T07:20:07Z 2013-04-08T07:20:07Z

<p>I am a physics student, for some physical property, I am seeking a manifold with nonzero pontryagin number. And I was told CP(2) is the simplest example which has $p_1(CP(2))=3$. </p> <p>Is there a nice(nice mean accessible to a non-mathematician) picture to show why this manifold has nonzero pontryagin number? And why a sphere $S^4$ does not. What's special for a complex projective plan. I don't know much about characteristic class.</p> <p>Forgive me if this question is too naive to mathematicians.</p>

http://mathoverflow.net/questions/115866/homotopy-pi-4su2z-2 Yingfei Gu 2012-12-09T01:24:40Z 2012-12-10T17:20:49Z

<p>I am a physics student, recently I read a paper using Homotopy $\pi_4(SU(2))=Z_2$, I guess mathematicians have some <strong>visualization or explanation</strong> of this result. So I come here ask for help. </p> <p>CROSS-POST from <a href="http://physics.stackexchange.com/questions/46284/homotopy-pi-4su2-z-2" rel="nofollow">http://physics.stackexchange.com/questions/46284/homotopy-pi-4su2-z-2</a></p>

http://mathoverflow.net/questions/115866/homotopy-pi-4su2z-2/115995#115995 Yingfei Gu 2012-12-11T10:09:08Z 2012-12-11T10:09:08Z

Thank you! This is a very very nice answer~

http://mathoverflow.net/questions/115866/homotopy-pi-4su2z-2 Yingfei Gu 2012-12-09T06:01:54Z 2012-12-09T06:01:54Z

@Alexander, got it. Thanks for reminding.

http://mathoverflow.net/questions/115866/homotopy-pi-4su2z-2 Yingfei Gu 2012-12-09T04:55:33Z 2012-12-09T04:55:33Z

BTW, thank you for inform me of the misuse of $\Pi,\pi$.

http://mathoverflow.net/questions/115866/homotopy-pi-4su2z-2 Yingfei Gu 2012-12-09T04:54:27Z 2012-12-09T04:54:27Z

Thank you for your responses. I guess the best way for me to understand is from the generator of $\pi_4(S^3)$. I googled and get some visualization of Hopf map, but now can you give me some &quot;visualization&quot; or explanation on the &quot;suspension homomorphism&quot;. @Sm Nlen @Tyler Lawson