$\hat{A}$ genus of total space of fiber bundle - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T07:44:04Z http://mathoverflow.net/feeds/question/96179 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/96179/hata-genus-of-total-space-of-fiber-bundle $\hat{A}$ genus of total space of fiber bundle MG 2012-05-07T03:22:38Z 2012-05-07T07:50:29Z <p>Is there any formula for calculate the $\hat{A}$ genus for the total space of a fiber bundle?</p> http://mathoverflow.net/questions/96179/hata-genus-of-total-space-of-fiber-bundle/96189#96189 Answer by Ping for $\hat{A}$ genus of total space of fiber bundle Ping 2012-05-07T07:26:01Z 2012-05-07T07:26:01Z <p>If the fiber is spin and the structure group of this fiber bundle is a compact, connected Lie group, then the $\hat{A}$ genus of the total space is the product of those of the base space and the fiber. Note that $\hat{A}$ genus is a very special case of the elliptic genera, the above-mentioned property is still true you we replace $\hat{A}$ gneus by an arbitrary elliptic genus.</p>