Norio Iwase
Mailing Adress: Faculty of Mathematics, Kyushu University, Motooka 744, Fukuoka 819-0395, Japan
E-mail Adress: iwase_AT__AT_math.kyushu-u.ac.jp
Authors.
myself
Preprint.
Abstract.
Jim Stasheff gave two apparently distinct definitions of an Am form, m ≤ ∞ in [17,18]. It is also claimed that the two definitions are equivalent in [17,18], while it is not apparently clear for us. That is why we are trying to clarify related things and to show that the claim is actually true under a `loop-like' hypothesis in this paper. Along with these two definitions, we must construct Associahedra and Multiplihedra as convex polytopes with piecewise-linearly decomposed faces to manipulate units in A∞ form. This is done in Iwase [9,10], Iwase-Mimura [11] or by Haiman [8] especially on Associahedra, followed recently by Forcey [7] and Mau-Woodward [14], while the origin of Associahedra goes back to Tamari [19]. In this paper, we follow [11] on the geometric construction of Associahedra and Multiplihedra as polytopes on the (half) lattice by taking a shadow or collecting words from trivalent or bearded trees.
- Associahedra, Multiplihedra and units in A∞ form (adobe-pdf file, 595KB)