Chillingworth found an algorithm for determining whether a given element of the fundamental group of a surface contains simple closed curves. We extend the theory to ‘open’ curves on a punctured surface.
@article{1147883397,
author = {Homma, Masahira},
title = {An algorithm for determining the simplicity of (i, j)-curves on a surface},
journal = {Hiroshima Math. J.},
volume = {36},
number = {1},
year = {2006},
pages = { 61-76},
language = {en},
url = {http://dml.mathdoc.fr/item/1147883397}
}
Homma, Masahira. An algorithm for determining the simplicity of (i, j)-curves on a surface. Hiroshima Math. J., Tome 36 (2006) no. 1, pp. 61-76. http://gdmltest.u-ga.fr/item/1147883397/