Geodesic
Automorphisms of Fuchsian Groups and their Lifts to Free Groups
Canadian journal of mathematics, Tome 41 (1989) no. 1, pp. 123-131

Voir la notice de l'article provenant de la source Cambridge University Press

This paper has been motivated by earlier work of the first two authors (see [3] ), where distinct Nielsen classes of generating systems for a Fuchsian group have been established and, in the case of odd and pairwise relative prime exponents π(i),classified. As a consequence they could distinguish nonisotopic Heegaard decompositions of Seifert fibred 3-manifolds. In proving that these decompositions are actually non-homeomorphic (see [3], Section 2), they investigated the question whether the different Nielsen classes of generating systems for G remain distinct, if one passes over to the weaker notion of “Nielsen equivalence up to automorphisms” (see [12], p. 3.5, 4.11 a-c): this means that the automorphisms of G are added to the Nielsen equivalence relations on the generators. 
Lustig, Martin; Moriah, Yoav; Rosenberger, Gerhard. Automorphisms of Fuchsian Groups and their Lifts to Free Groups. Canadian journal of mathematics, Tome 41 (1989) no. 1, pp. 123-131. doi: 10.4153/CJM-1989-006-1
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