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Zbl 0968.32009
Tessellations of moduli spaces and the mosaic operad.
(English)
[A] 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). ISBN 0-8218-1057-X/pbk

The author studies the geometry and topology of the real points~$\overline{{\cal M}_0^n}(\Bbb R)$ of a certain compactification of the moduli space of Riemann spheres with $n$~punctures~${\cal M}_0^n(\Bbb C)$. 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 $\overline{{\cal M}_0^n}(\Bbb R)$ can be tesselated by $1/2\cdot(n-1)!$ associahedra of dimension~$n-3$. This gives a formula for the Euler characteristic of~$\overline{{\cal M}_0^n}(\Bbb R)$. The combinatorics of associahedra is further used to investigate the relationship by blow-ups between $\overline{{\cal M}_0^n}(\Bbb R)$ and the projective space PG$_{n-3}\Bbb R$.
[Michael Joswig (Berlin)]
MSC 2000:
*32G15 Teichmüller theory

Keywords: moduli space; configuration space; complex projective line; associahedron

Cited in: Zbl 1231.32010 Zbl 1206.14051

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