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Lines and circles meeting links
by
Julia Viro
Uppsala University (Uppsala, Sweden)
We will consider low bounds for the number of lines meeting given 4 disjoint smooth closed curves in the real projective 3-space in a given cyclic order. Similarly, we estimate the number of circles meeting in a given cyclic order given 6 disjoint smooth closed curves in Euclidean 3-space. The estimations are formulated in terms of linking numbers of the curves and based on a study of a surface swept by projective lines meeting 3 given disjoint smooth closed curves and a surface swept by circles meeting 5 given disjoint smooth closed curves. These results admit generalizations to higher dimensions and more complicated patterns of intersections. Lines and circles can be replaced by configurations of curves of other kinds; linking numbers, by Vassiliev invariants.
Date received: February 4, 2005
Copyright © 2005 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # capo-21.