Self-intersections in combinatorial topology: statistical structure |
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Authors: | Moira Chas Steven P Lalley |
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Institution: | (1) University of Southern California, Los Angeles, CA 90089-2532, USA |
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Abstract: | Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic
words in the generators of the fundamental group and their inverses. By self-intersection number one means the minimum number
of transversal self-intersection points of representatives of the class. We prove that if a class is chosen at random from
among all classes of m letters, then for large m the distribution of the self-intersection number approaches the Gaussian distribution. The theorem was strongly suggested
by a computer experiment with four million curves producing a very nearly Gaussian distribution. |
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