Self-intersections in combinatorial topology: statistical structure

Details Self-intersections in combinatorial topology: statistical structure Self-intersections in combinatorial topology: statistical structure

2010-12-02

arxiv.org/abs/1012.0580v2

Mathematics

Geometric Topology

Minor revision of version 1

Scientific paper

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.

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