Lone axes in outer space

. G R ] 3 J ul 2 00 6 Axes in Outer Space

We develop a notion of axis in the Culler–Vogtmann outer space Xr of a finite rank free group Fr, with respect to the action of a nongeometric, fully irreducible outer automorphism φ. Unlike the situation of a loxodromic isometry acting on hyperbolic space, or a pseudo-Anosov mapping class acting on Teichmüller space, Xr has no natural metric, and φ seems not to have a single natural axis. Inst...

Plants circling in outer space

Plants do not grow in a strict linear manner, rather they circumnutate. That is, they exhibit an oscillatory or helical growth pattern around an axis. Circumnutation is readily apparent in vines such as morning glory or grape (Fig. 1), but in fact it is nearly ubiquitous in plants. Circumnutation occurs in almost all plant organs throughout all stages of development (Johnsson, 1997; Larson, 200...

Developmental Biology in Outer Space

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Contracting orbits in Outer space

We show that strongly contracting geodesics in Outer space project to parameterized quasigeodesics in the free factor complex. This result provides a converse to a theorem of Bestvina– Feighn, and is used to give conditions for when a subgroup of Out(F) has a quasi-isometric orbit map into the free factor complex. It also allows one to construct many new examples of strongly contracting geodesi...

Plants circling in outer space.