2-associahedra

Abstract

For any $r\ge 1$ and $\mathbf{n}\in {\mathbb{Z}}_{\ge 0}^r\setminus \{0\}$ we construct a poset $W_{\mathbf{n}}$ called a 2-associahedron. The 2-associahedra arose in symplectic geometry, where they are expected to control maps between Fukaya categories of different symplectic manifolds. We prove that the completion $\widehat{W_{\mathbf{n}}}$ is an abstract polytope of dimension $|\mathbf{n}|+r-3$. There are forgetful maps $W_{\mathbf{n}}\to K_r$, where $K_r$ is the $(r-2)$-dimensional associahedron, and the 2-associahedra specialize to the associahedra (in two ways) and to the multiplihedra. In an appendix, we work out the 2- and 3-dimensional associahedra in detail.

49 pages, 51 figures. Final version to be published in Algebraic & Geometric Topology

References in corpus (1)

• A-infinity functors for Lagrangian correspondences

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