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Classification of lifts of automorphisms of surfaces to the unit disk. (English) Zbl 0822.57010
McCord, Christopher K. (ed.), Nielsen theory and dynamical systems. AMS- IMS-SIAM summer research conference, June 20-26, 1992, South Hadley, MA (USA), supported by the National Science Foundation. Providence, RI: American Mathematical Society. Contemp. Math. 152, 311-340 (1993).
From the author’s introduction: “The goal of this paper is to prove J. Nielsen’s results [Topology of closed orientable surfaces II, Collected Mathematical Papers, Vol. 1 (1986; Zbl 0609.01050)] on the fixed points of lifts of automorphisms of a compact surface \(S\) with boundary of genus \(p\) \((p>1)\) to its universal covering space (the unit disk \(U\)), on its boundary \(\partial U\) based on W. Thurston’s classification theorem [Bull. Am. Math. Soc., New Ser. 19, No. 2, 417-431 (1988; Zbl 0674.57008)] for automorphisms of surfaces. Therefore our work can be seen as complementary to the results of R. T. Miller [Adv. Math. 45, 189-212 (1982; Zbl 0496.57003)] and of M. Handel and W. P. Thurston [ibid. 56, 173-191 (1985; Zbl 0584.57007)] who showed that Thurston’s theorem follows from the Nielsen theory”.
For the entire collection see [Zbl 0780.00035].

MSC:
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57S30 Discontinuous groups of transformations
30F60 Teichm├╝ller theory for Riemann surfaces
57R50 Differential topological aspects of diffeomorphisms
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