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SELF-INTERSECTION NUMBERS OF PATHS IN COMPACT SURFACES

LORENA ARMAS-SANABRIA

Universidad Autónoma Metropolitana, Unidad Cuajimalpa, Artificios 40, Col. Miguel Hidalgo, 01120 México D.F., Mexico

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FRANCISCO GONZÁLEZ-ACUÑA

Instituto de Matemáticas, Universidad Nacional Autónoma de México Ciudad Universitaria, 04510 México D.F., Mexico

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JESÚS RODRÍGUEZ-VIORATO

Instituto de Matemáticas, Universidad Nacional Autónoma de México Ciudad Universitaria, 04510 México D.F., Mexico

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https://doi.org/10.1142/S0218216511008826Cited by:3 (Source: Crossref)

Abstract

In this paper, we give an algorithm to calculate the minimal self-intersection number of paths in a compact surface with boundary representing a given element of the free group F(x₁, x₂, …, x_n). In particular, this algorithm says whether or not a word in x₁, x₂, …, x_n is representable by a simple path. Our algorithm is simpler than similar algorithms given previously. In the case of a disk with n holes the problem is equivalent to the problem of deciding which relators can appear in an Artin n-presentation.

Keywords:

AMSC: 57M99, 57M05

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