RELATIVE TWISTING IN OUTER SPACE

Twisting and Turning in Space

ion and classification continues, What's Euclidean On a perfectly flat surface, parallel lines never meet. A triangle drawn on such a plane has interior angles that add up to 1800. A straight line is the shortest distance between two points. These and other postulates and results are part of the geometry first invented by Euclid more than 2,000 years ago. Later mathematicians refined and extend...

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.