Geometric realizations of the multiplihedron and its complexification

Abstract

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.

v4. 27 pages, 19 figures. Incorporated referee comments

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