Cartan 3-form on a Lie group G - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T11:44:06Z http://mathoverflow.net/feeds/question/62998 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/62998/cartan-3-form-on-a-lie-group-g Cartan 3-form on a Lie group G Kevin Wray 2011-04-26T03:58:26Z 2011-04-26T04:28:16Z <p>Does anyone have a reference to learn more about the Cartan $3$-form on a group manifold $G$? I have read that the WZW term is nothing more than the integral of the pullback of the Cartan $3$-form via $g:W\rightarrow G$</p> <p>$WZW = -\frac{1}{6}\int_W \langle \phi_g\wedge[\phi_g\wedge\phi_g]\rangle$,</p> <p>where $\phi_g=g^\ast(\phi)$ is the pullback of the Maurer-Cartan form, and would like to learn more about the math behind WZW terms. For eg., why is it the generator of $H^3(G,\mathbb{R})$ when $G$ is a connected, simply connected, compact Lie group?</p>