For a closed orientable surface S, any map f : S→S whose n-th power is homotopic to the identity, is homotopic to a homeomorphism g of S of order n. This famous theorem of Nielsen is known to fail in general for aspherical manifolds. In this paper, for model aspherical manifolds M associated to a finitely extendable set of data, we, however, present a weaker version of Nielsen’s result. We show...

We consider germs of conformal mappings tangent to the identity at the origin in C. We construct a germ of a homeomorphism which is a C∞ diffeomorphism except at the origin conjugating these holomorphic germs with the time-one map of the vector field V (z) = zm ∂ ∂z . We then show that, in the case m = 2, for a germ of a homeomorphism which is real-analytic in a punctured neighborhood of the or...

We study full groups ofminimal actions of countable groups by homeomorphisms on a Cantor space X, showing that these groups do not admit a compatible Polish group topology and, in the case of Z-actions, are coanalytic non-Borel inside Homeo(X). We then focus on the closure of the full group of a uniquely ergodic homeomorphism, elucidating underwhich conditions this group has a comeager (or, equ...

A homeomorphism of a 3-manifold M is said to be Dehn twists on the boundary when its restriction to ∂M is isotopic to the identity on the complement of a collection of disjoint simple closed curves in ∂M . In this paper, we give various results about such collections of curves and the associated homeomorphisms. In particular, if M is compact, orientable, irreducible and ∂M is a single torus, an...

We present two examples of nice normal spaces X having the property that for some fixedpoint free homeomorphism on X its tech-Stone extension has a fixed point. One of the spaces presented here is locally countable, locally compact, separable, normal, countably paracompact and weakly zero-dimensional. The other one is hereditarily normal and strongly zero-dimensional. Our construction of this e...