Remarks on flat $S^1$-bundles, $C^{\infty }$ vs $C^{\omega }$

Teruaki Kitano, Yoshihiko Mitsumatsu, Shigeyuki Morita

We describe low dimensional homology groups of ${\mathrm{Diff}}_{+}^{\delta }{S}^1$ in terms of Haefliger's classifying space $B{\overline{\Gamma }}_1$ by applying a theorem of Thurston. Then we consider…