Classification of three-dimensional mappings with surface pseudo-Anosov dynamics

The paper is concerned with orientation-preserving homeomorphisms of 3-manifolds with nonwandering set consisting of a finite number of two-dimensional attractors and repellers, each of which is a disjoint union of cylindrically embedded closed surfaces such that the restriction of some power of the homeomorphism to each surface is topologically conjugate to an orientation-preserving pseudo-Anosov homeomorphism. A topological classification is obtained for the model homeomorphisms realized on each manifold allowing homeomorphisms of the class under study. A homeomorphism in the class under consideration is shown to be topologically conjugate to a model map if and only if its has an invariant one-dimensional foliation. If conjugacy to generalized pseudo-Anosov homeomorphisms on the nonwandering sets of maps under study is allowed, then examples of homeomorphisms are presented whose restrictions to connected components of the nonwandering set are not topologically conjugate, which is uncharacteristic for homeomorphisms in the original class under consideration. Bibliography: 16 titles.