Intrinsic characteristic classes of a local Lie group

Abstract

For a local Lie group $M$ we define cohomology classes $[w_{2k+1}]\in H_{dR}^{2k+1}(M,R)$. We show that $[w_1]$ is an obstruction to globalizability and give an example where $[w_1]\ne 0$. We also show that $[w_3]$ coincides with Godbillon–Vey class in a particular case. These classes are secondary as they emerge when curvature vanishes.