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Automorphisms of Fuchsian Groups and their Lifts to Free Groups

Published online by Cambridge University Press:  20 November 2018

Martin Lustig ,
Yoav Moriah  and
Gerhard Rosenberger
Martin Lustig
Affiliation:
Ruhr-Universität Bochum, Bochum, West Germany
Yoav Moriah
Affiliation:
Technion, Haifa, Israel
Gerhard Rosenberger
Affiliation:
Universität Dortmund, Dortmund, West Germany
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 1 , 01 February 1989 , pp. 123 - 131
Copyright
Copyright © Canadian Mathematical Society 1989

References

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