Tessellations of Moduli Spaces and the Mosaic Operad
Satyan L. Devadoss
Primary: 14H10
Secondary: 05B45, 52B11
Department of Mathematics
Johns Hopkins University
Baltimore, MD 21218
devadoss@math.jhu.edu
The following are all EPS files:
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Abstract:
We construct a new (cyclic) operad of \emph{mosaics} defined by polygons with marked diagonals. Its underlying (aspherical) spaces are the sets \overline{\mathcal {M}}^n_0({\mathbb R}) of real points of the moduli space of punctured stable curves of genus zero, 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.