Geometric realizations of the multiplihedron and its complexification

Mathematics – Geometric Topology

Scientific paper

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v4. 27 pages, 19 figures. Incorporated referee comments

Scientific paper

We realize Stasheff's multiplihedron geometrically as the moduli space of
stable quilted disks. This generalizes the geometric realization of the
associahedron as the moduli space of stable disks. We show that this moduli
space is the non-negative real part of a complex moduli space of stable scaled
marked curves.

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