The expected genus of a random chord diagram

Details The expected genus of a random chord diagram The expected genus of a random chord diagram

2009-04-28

arxiv.org/abs/0904.4361v1

Mathematics

Geometric Topology

Scientific paper

To any generic curve in an oriented surface there corresponds an oriented chord diagram, and any oriented chord diagram may be realized by a curve in some oriented surface. The genus of an oriented chord diagram is the minimal genus of an oriented surface in which it may be realized. Let g_n denote the expected genus of a randomly chosen oriented chord diagram of order n. We show that g_n satisfies: g_n = n/2 - Theta(ln n).

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