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When a low dimensional chaotic attractor is embedded in a three dimensionalspace its topological properties are embedding-dependent. We show that thereare just three topological properties that depend on the embedding: parity,global torsion, and knot type. We discuss how they can change with theembedding. Finally, we show that the mechanism that is responsible for creatingchaotic behavior is an invariant of all embeddings. These results apply only tochaotic attractors of genus one, which covers the majority of cases in whichexperimental data have been subjected to topological analysis. This means thatthe conclusions drawn from previous analyses, for example that the mechanismgenerating chaotic behavior is a Smale horseshoe mechanism, a reversehorseshoe, a gateau roule, an S-template branched manifold, ..., are notartifacts of the embedding chosen for the analysis.

Embeddings of low-dimensional strange attractors: Topological invariants and degrees of freedom