Oriented Cobordism Rings - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T09:30:46Z http://mathoverflow.net/feeds/question/26655 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/26655/oriented-cobordism-rings Oriented Cobordism Rings JuanSOS 2010-06-01T02:27:38Z 2010-06-01T07:45:22Z <p>Hey everybody! I was wondering if anybody had available the calculation of the Oriented cobordism groups in dimensions higher than 10? Or if anybody knew if there is another kind of torsion beside 2-torsion in them? (e.g. I know that \$\Omega^5\$ is \$\mathbb{Z}_2\$, is there a group with n-torsion with n distinct from 2?). Thanx, Refferences are also appreciated....</p> http://mathoverflow.net/questions/26655/oriented-cobordism-rings/26656#26656 Answer by Tyler Lawson for Oriented Cobordism Rings Tyler Lawson 2010-06-01T02:43:52Z 2010-06-01T02:43:52Z <p>There is no torsion other than 2-primary torsion in the oriented bordism ring. One has that after inverting 2, the oriented bordism ring is a polynomial algebra on generators in degrees which are multiples of 4: <code>\$\$ \Omega^{SO}_*[1/2] = \mathbb{Z}[1/2, x_4, x_8, x_{12}, \ldots] \$\$</code> If I remember correctly, this (and the answers to many bordism-related questions) can be found in Stong's "Notes on cobordism theory".</p> http://mathoverflow.net/questions/26655/oriented-cobordism-rings/26678#26678 Answer by Thorny for Oriented Cobordism Rings Thorny 2010-06-01T07:45:22Z 2010-06-01T07:45:22Z <p>I would also recommend Wall's <a href="http://www.jstor.org/stable/1970136" rel="nofollow">Determination of the cobordism ring</a> as a more primary source, it also contains the fact that all torsion is of order 2.</p>