Return words of linear involutions and fundamental groups
Abstract
We investigate the shifts associated with natural codings of linear in-volutions. We deduce from the geometric representation of linear invo-lutions 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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