### Second cohomology classes of the group of ${C}^{1}$-flat diffeomorphisms

Tomohiko Ishida (2012)

Annales de l’institut Fourier

Similarity:

We study the cohomology of the group consisting of all ${C}^{\infty}$-diffeomorphisms of the line, which are ${C}^{1}$-flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.