Classification of Partially Hyperbolic Diffeomorphisms in 3-manifolds with Solvable Fundamental Group

Weakly Hyperbolic Actions of Kazhdan Groups on Tori

We study the ergodic and rigidity properties of weakly hyperbolic actions. First, we establish ergodicity for C2 volume preserving weakly hyperbolic group actions on closed manifolds. For the integral action generated by a single Anosov diffeomorphism this theorem is classical and originally due to Anosov. Motivated by the Franks/Manning classification of Anosov diffeomorphisms on tori, we rest...

An Introduction to 3-manifolds

Introduction In these lecture notes we will give a quick introduction to 3–manifolds, with a special emphasis on their fundamental groups. The lectures were held at the summer school 'groups and manifolds' held in Münster July 18 to 21 2011. In the first section we will show that given k ≥ 4 any finitely presented group is the fundamental group of a closed k–dimensional man-ifold. This is not t...

An Introduction to 3-manifolds and Their Fundamental Groups

In these lecture notes we will give a quick introduction to 3-manifolds, with a special emphasis on their fundamental groups. In the first section we will show that given k ≥ 4 any finitely presented group is the fundamental group of a closed, oriented k–dimensional manifold. This is not the case for 3-manifolds. For example we will see that Z,Z/n,Z ⊕ Z/2 and Z are the only abelian groups which...

Pointwise Partial Hyperbolicity in 3-dimensional Nilmanifolds

We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds with nilpotent, non-abelian fundamental group. We further classify the partially hyperbolic systems on these manifolds up to leaf conjugacy. We also classify those systems on the 3-torus which do not have an attracting...

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds