Diagonals on the Permutahedra, Multiplihedra and Associahedra

Associahedra、Multiplihedra与$A_{\infty}$形式中的单位

Associahedra, Multiplihedra and units in $A_{\infty}$ form

本文通过构造$A_{m}$-结构并引入internal precategory理论，重新证明了$A_{\infty}$形式中两个单位定义在“loop-like”条件下的等价性。

四类associahedra模型之间的等价性

Equivalence Between Four Models of Associahedra

本文研究了四类associahedra模型之间的等价性，揭示了Stasheff associahedra与Loday构造的同构关系，并探讨了multiplihedra和graph cubeahedra之间的联系。

The diagonal of the multiplihedra and the tensor product of A-infinity morphisms

We define a cellular approximation for the diagonal of the Forcey--Loday realizations of the multiplihedra, and endow them with a compatible topological cellular operadic bimodule structure over the Loday realizations of the associahedra. This provides us with a model for topological and algebraic A-infinity morphisms, as well as a universal and explicit formula for their tensor product. We study the monoidal properties of this newly defined tensor product and conclude by outlining several applications, notably in algebraic and symplectic topology.

排列多面体的胞腔对角线

Cellular diagonals of permutahedra

本文系统研究排列多面体的几何胞腔对角线，通过超平面排列对偶得到计数结果，刻画与operad结构相容的两条同构对角线的性质，并由此推出operahedra与multiplihedra上的两类拓扑胞腔operad结构及两类几何泛张量积。