Tessellations of Moduli Spaces and the Mosaic Operad

Details Tessellations of Moduli Spaces and the Mosaic Operad Tessellations of Moduli Spaces and the Mosaic Operad

1998-07-02

arxiv.org/abs/math/9807010v2

Contemporary Mathematics Volume 239

Mathematics

Algebraic Geometry

24 pages, 26 figures, LaTex; updated and improved content (1999)

Scientific paper

We construct a new (cyclic) operad of `mosaics' defined by polygons with marked diagonals. Its underlying (aspherical) spaces are the sets of real points of the moduli space of punctured Riemann spheres, which are naturally tiled by Stasheff associahedra. We (combinatorially) describe them as iterated blow-ups and show that their fundamental groups form an operad with similarities to the operad of braid groups.

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