Partially Hyperbolic Dynamics and 3-Manifold Topology

Robust Ergodic Properties in Partially Hyperbolic Dynamics

We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana [BV] about existence and finitude of physical measures is extended to the case of local diffeomorphisms. Moreover, we prove that such systems constitute a C2-open set in which statistical stability is a dense property. In contrast, all mostly contracting syst...

Notes on Basic 3-Manifold Topology

These notes, originally written in the 1980’s, were intended as the beginning of a book on 3 manifolds, but unfortunately that project has not progressed very far since then. A few small revisions have beenmade in 1999 and 2000, butmuchmore remains to be done, both in improving the existing sections and in adding more topics. The next topic to be added will probably be Haken manifolds in §3.2. ...

Introducing Regina, The 3-Manifold Topology Software

An overview is presented of Regina, a freely available software package for 3-manifold topologists. In addition to working with 3-manifold triangulations, Regina includes support for normal surfaces and angle structures. The features of the software are described in detail, followed by examples of research projects in which Regina has been used.

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds

A Note on Quantum 3-manifold Invariants and Hyperbolic Volume

For a closed, oriented 3-manifold M and an integer r > 0, let τr(M) denote the SU(2) Reshetikhin-Turaev-Witten invariant of M , at level r. We show that for every n > 0, and for r1, . . . , rn > 0 sufficiently large integers, there exist infinitely many non-homeomorphic hyperbolic 3-manifolds M , all of which have different hyperbolic volume, and such that τri(M) = 1, for i = 1, . . . , n.