most recent 30 from http://mathoverflow.net 2013-05-25T20:25:57Z http://mathoverflow.net/feeds/question/63470 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/63470/third-bordism-group-of-bg-where-g-is-an-arbitrary-compact-lie-group Kevin Wray 2011-04-29T20:27:13Z 2011-04-29T21:46:46Z

<p>Is anything known about $\Omega_3(BG)$, where $G$ is an arbitrary compact Lie group; i.e., is it possible to describe the structure of $\Omega_3(BG)$ for any compact Lie group? I know that $H_3(BG)$ consists completely of torsion when $G$ is compact and I would like (if possible) a similar type of statement for $\Omega_3(BG)$.</p>

http://mathoverflow.net/questions/63470/third-bordism-group-of-bg-where-g-is-an-arbitrary-compact-lie-group/63478#63478 Johannes Ebert 2011-04-29T21:46:46Z 2011-04-29T21:46:46Z

<p>If you think about oriented bordism, the answer is that $\Omega_3 (BG) \cong H_3 (BG)$. This is true for any space $X$ instead of $BG$, because of the Atiyah-Hirzebruch spectral sequence and because $\Omega_i (pt)=0$ for $i=1,2,3$.</p>