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Tessellations of moduli spaces and the mosaic operad. (English) Zbl 0968.32009
Meyer, Jean-Pierre (ed.) et al., Homotopy invariant algebraic structures. A conference in honor of J. Michael Boardman. AMS special session on homotopy theory, Baltimore, MD, USA, January 7-10, 1998. Providence, RI: American Mathematical Society. Contemp. Math. 239, 91-114 (1999).
The author studies the geometry and topology of the real points  0 n ¯() of a certain compactification of the moduli space of Riemann spheres with n punctures  0 n (). It is known that the latter can be identified with the configuration space of n distinct points on the complex projective line modulo the action of the group of Möbius transformations. The author proves that 0 n ¯() can be tesselated by 1/2·(n-1)! associahedra of dimension n-3. This gives a formula for the Euler characteristic of  0 n ¯(). The combinatorics of associahedra is further used to investigate the relationship by blow-ups between 0 n ¯() and the projective space PG n-3 .

32G15Moduli of Riemann surfaces, Teichmüller theory