On the Magnus Function
Roger C. Alperin
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1 Introduction
There are uncountably many integer functions M : Z ¡! Z having the
properties
M(0) = 0;M(M(x)) = x;M(x) = M(M(x ¡ 1) ¡ 1) ¡ 1:
Using this B. Neumann [cf. M2] showed the existence of uncountably many
maximal non-parabolic subgroups of the modular group PSL2(Z).
J. Marklof. (2004)cite arxiv:math/0407288
Comment: Lectures given at the International School "Quantum Chaos on
Hyperbolic Manifolds" (Schloss Reisensburg, Gunzburg, Germany, 4-11 October
2003). To appear in Springer LNP.
Y. Algom-Kfir, and M. Bestvina. (2009)cite arxiv:0910.5408
Comment: 15 pages, accepted to Geometriae Dedicata, omitted the comment about
the potential function in rank 2 being equal to injrad (because it was false).
Łukasz Garncarek. (2010)cite arxiv:1008.1275
Comment: (v1) 5 pages; (v2) 7 pages; a substantially rewritten version;
improved presentation; some new material on induced representations; removed
the "Another approach..." section.
M. Bridson, and K. Vogtmann. (2010)cite arxiv:1007.2598
Comment: Incorrect Lemma (2.5) replaced by new Proposition 2.5. Typos
corrected, references updated.
F. Bonahon, and H. Wong. (2010)cite arxiv:1003.5250
Comment: 40 pages, 25 figures. Version 2: Fixed classical case. Misprints
corrected. Version 3: More misprints corrected, including statement of Lemma
22. Added observation that the quantum trace homomorphism is injective.
Version 4: Final corrections before submission.