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Geometric realizations of the multiplihedra

Part of:Polytopes and polyhedraCategories with structureCurves

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: sikimeti@msri.org)
C. Woodward
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA (email: ctw@math.rutgers.edu)
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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: Operads14H10: Families, moduli (algebraic)52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry)

Information

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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