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By Schaller P. S.

Geometric And useful AnalysisVolume eleven, number one 2001 г.

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11, 2001 ¨ CELL DECOMPOSITION OF TEICHMULLER SPACE 171 Let t be a common orthogonal in M between b and e. Then M ∈ M in(F ) if and only if s and t can be chosen so that they lie in Q and moreover cos α cos γ > cos β cos δ holds. The latter condition can also be formulated as follows. Let ζ be the angle between s and t which contains the vertex of Q between b and c as well as the vertex of Q between d and a. Then ζ < π/2. (c) (2, 0)-surfaces. Definition. A septuple is a set F of seven simple closed geodesics in a (2, 0)-surface which contains two quintuples such that the intersections are as for the set of seven elements in Figure 3.

52 (1999), 407–452. [S4] P. Schmutz Schaller, A systolic geometric cell decomposition for the space of once-holed Riemann surfaces of genus 2, Topology, to appear. [S5] P. Schmutz Schaller, Riemann surfaces with longest systole and an improved Vorono¨ı algorithm, Arch. , to appear. [ScL1] L. Schneps, P. Lochak, Geometric Galois Actions. 1. Around Grothendieck’s esquisse d’un programme, London Math. Soc. Lecture Note Series 242, Cambridge University Press (1997). [ScL2] L. Schneps, P. Lochak, Geometric Galois Actions.

11, 2001 ¨ CELL DECOMPOSITION OF TEICHMULLER SPACE 173 [HatLS] A. Hatcher, P. Lochak, L. Schneps, On the Teichm¨ uller tower of mapping class groups, J. Reine Angew. Math. 521 (2000), 1–24. [HatT] A. Hatcher, W. Thurston, A presentation of the mapping class group of a closed orientable surface, Topology 19 (1980), 221–239. V. Ivanov, Complexes of curves and the Teichm¨ uller modular group, Uspekhi Mat. Nauk 42 (1987), 43–91; English transl. Russian Math. Surveys 42 (1987), 55–107. P. Kerckhoff, The Nielsen realization problem, Ann.

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