Genus two Smale-Williams solenoids in 3-manifolds

Details Genus two Smale-Williams solenoids in 3-manifolds Genus two Smale-Williams solenoids in 3-manifolds

2006-10-16

arxiv.org/abs/math/0610474v2

Mathematics

Geometric Topology

18 pages, corrected typos

Scientific paper

Using alternating Heegaard diagrams, we construct some 3-manifolds which admit diffeomorphisms such that the non-wandering sets of the diffeomorphisms are composed of Smale-Williams solenoid attractors and repellers, an interesting example is the truncated-cube space. In addition, we prove that if the nonwandering set of the diffeomorphism consists of genus two Smale-Williams solenoids, then the Heegaard genus of the closed manifold is at most two.

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