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By Schaller P. S.

Geometric And practical AnalysisVolume eleven, number one 2001 г.

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Ann. of Math. Studies 97, Princeton University Press (1981), 245–251. [Hat] A. Hatcher, On triangulations of surfaces, Topology Appl. 40 (1991), 189–194. Vol. 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.

Math. 132 (1998), 607–632. [Mo] S. Morita, Problems on the structure of the mapping class group of surfaces and the topology of the moduli space of curves, in “Topology, Geometry and Field Theory” (K. , eds). World Scientific Singapore (1994), 101–110. [Mos1] L. Mosher, Tiling the projective foliation space of a punctured surface, Trans. Amer. Math. Soc. 306 (1988), 1–70. [Mos2] L. Mosher, Mapping class groups are automatic, Ann. of Maths. 142 (1995), 303–384. B. Patterson, Teichm¨ uller spaces are distinct, Proc.

C. Penner, The decorated Teichm¨ uller space of punctured surfaces, Commun. Math. Phys. 113 (1987), 299–339. [S1] P. Schmutz, Riemann surfaces with shortest geodesic of maximal length, Geom. Funct. Anal. 3 (1993), 564–631. [S2] P. Schmutz Schaller, Geometry of Riemann surfaces based on closed 174 P. SCHMUTZ SCHALLER GAFA geodesics, Bull. Am. Math. Soc. 35 (1998), 193–214. P. Schmutz Schaller, Systoles and topological Morse functions for Riemann surfaces, J. Differential Geom. 52 (1999), 407–452.

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A cell decomposition of Teichmuller space based on geodesic length functions by Schaller P. S.

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