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Return words of linear involutions and fundamental groups
Published online by Cambridge University Press: 28 December 2015
Abstract
We investigate the shifts associated with natural codings of linear involutions. We deduce, from the geometric representation of linear involutions as Poincaré maps of measured foliations, a suitable definition of return words which yields that the set of return words to a given word is a symmetric basis of the free group on the underlying alphabet,
$A$
. The set of return words with respect to a subgroup of finite index
$G$
of the free group on
$A$
is also proved to be a symmetric basis of
$G$
.
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- Research Article
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- © Cambridge University Press, 2015
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