Great circle links in the three-sphere

Details Great circle links in the three-sphere Great circle links in the three-sphere

2003-08-06

arxiv.org/abs/math/0308048v1

Mathematics

Geometric Topology

Dissertation for degree awarded June 17, 2003 from UC Davis, 50 pages, 18 figures

Scientific paper

We investigate great circle links in the three-sphere, the class of links where each component is a great circle. Using the geometry of their complements, we classify such links up to five components. For any two-bridge knot complement, there is a finite cover that is the complement of a link of great circles in $S^3$. We show that for many two-bridge knots, this cover contains a closed incompressible surface. Infinitely many fillings of the two-bridge knot lift to fillings of great circle link where the incompressibility of this surface is preserved. Using this, we show that infinitely many fillings of an infinite class of two-bridge knot complements are virtually Haken.

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