an:01997251
Zbl 1026.30037
Imayoshi, Yoichi; Ito, Manabu; Yamamoto, Hiroshi
On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces with two specified points
EN
Osaka J. Math. 40, No. 3, 659-685 (2003).
00098096
2003
j
30F10
Let \(S\) be a hyperbolic Riemann surfaces \(R\) of analytically finite type with two specific points \(p_1,p_2\in S\), and set \(\dot S:=S\setminus \{p_1,p_2\}\). Let \(I sot(S,2)\) be the group of orientation preserving homeomorphisms of \(S\) onto itself isotopic to \(id_S\) and fixing the \(p_j\) factored by the normal subgroup of homeomorphisms of \(S\) isotopic to the identity of \(\dot S\). Elements \([\omega]\in I sot(S,2)\) induce canonically elements \(\langle\omega |_S\rangle\) of the Teichm??ller modular group \(\text{Mod} (\dot S)\). \textit{L. Bers} [Acta Math. 141, 73-98 (1978; Zbl 0389.30018)] classified elements of \(\text{Mod}(\dot S)\) as elliptic, parabolic and elliptic using the Teichm??ller distance on the Teichm??ller space \(T(\dot S)\). In this paper the corresponding classification of elements \([\omega]\) of \(I sot(S,2)\) is described using the strings of the induced pure braids \([b_\omega]\). The results are motivated by a theorem of \textit{I. Kra} for surfaces with one specific point [Acta Math. 146, 231-270 (1981; Zbl 0477.32024)].
S.Timmann (Hannover)
Zbl 0389.30018; Zbl 0477.32024