Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

On the Euler class for flat S^1-bundles, C^\infty vs C^\omega

We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S^1 in terms of BΓ^1 by applying a theorem of Thurston. It is an open problem whether some power of the rational Euler class vanishes for real analytic flat S^1 bundles. In this talk we discuss that if it does, then the homology group should contain many torsion classes that vanish in the smooth case. Along this line we can give a new proof for the non-triviality of any power of the rational Euler class in the smooth case. If time permits, we will mention some attempts to study a Mather-Thurston map in the analytic case. This talk will be based on a joint work with Shigeyuki Morita and Yoshihiko Mitsuma