A class α and locally connected continua which can be ε-mapped onto a surface
We prove that the standard action of the mapping class group of a surface of sufficiently large genus on the unit tangent bundle is not homotopic to any smooth action.
An elementary proof of the following theorem is given:THEOREM. Let M be a compact connected surface without boundary. Consider a C∞ action of Rn on M. Then, if the Euler-Poincaré characteristic of M is non zero there exists a fixed point.
In this talk, we shall look at the application of Nielsen theory to certain questions concerning the "homotopy minimum" or "homotopy stability" of periodic orbits under deformations of the dynamical system. These applications are mainly to the dynamics of surface homeomorphisms, where the geometry and algebra involved are both accessible.