Associahedra, Multiplihedra and units in A_∞ form

Norio Iwase - Kyushu

Resumo:

Jim Stasheff gave two apparently distinct definitions for A_∞ form in his papers in '63 and '70. The latter paper claims that the two definitions are equivalent, while others including myself can not verify the proof. In this talk, we show that it is actually true in a slightly weaker form under small additional assumptions. To treat units in A_∞ form defined in '63, we need to construct Associahedra and Multiplihedra as convex polytopes with piecewise linear decompositions, which is performed in my master thesis in '83 or a paper with Mimura in '89, while we do not know much about the construction of Associahedra given in a unpublished work by Haiman in '84. We shall follow the construction of Associahedra and Multiplihedra in '89.

© Norio Iwase.