On representability of the smooth Euler class
On representability of the smooth Euler class
The Euler class, which lies in the second cohomology of the group of orientation preserving homeomorphisms of the circle, is pulled back to the "smooth'' Euler class in the cohomology of the group of orientation preserving smooth diffeomorphisms of the circle. Suppose a surface group $\Gamma$ (of genus $> 1$) …