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Geometric realizations of the multiplihedra

Part of: Curves Polytopes and polyhedra Categories with structure

Published online by Cambridge University Press:  12 May 2010

S. Ma’u  and
C. Woodward
S. Ma’u
Affiliation:
The Mathematics Sciences Research Institute, 17 Gauss Way, Berkeley, CA 94720-5070, USA (email: [email protected])
C. Woodward
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA (email: [email protected])
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Abstract

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We realize the 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.

Keywords

multiplihedronassociahedronnodal diskmetric treemoment polytope

MSC classification

Secondary: 18D50: Operads 14H10: Families, moduli (algebraic) 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry)
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 4 , July 2010 , pp. 1002 - 1028
Copyright
Copyright © Foundation Compositio Mathematica 2010

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