Seminar on low-dimensional mathematics
Friday, July 11, 2008

Tangents to spheres and transversals to balls
Ciprian Borcea, Rider University, Lawrenceville, USA

A generic configuration of three spheres can be reconstructed from the
complex sextic curve which records the direction of common tangents. The
real direction-sextic is also useful in proving a convexity result which
implies the following theorem: "The connected components in the space of
line transversals to disjoint balls can be labeled by the geometric
permutations associated to them." A geometric permutation is the pair of
orderings of the (numbered) balls determned by a transversal with its two
orientations.

Reference: C. Borcea, X. Goaoc, S. Petitjean: "Line transversals to disjoint
balls", Discrete and Computational Geometry, March 2008.
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Home-page of the seminar: http://www.pdmi.ras.ru/~lowdimma