Nathaniel Bottman
2019 Algebraic and Geometric Topology  
For any r≥ 1 and n∈Z_≥0^r ∖{0} we construct a poset W_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 W_n is an abstract polytope of dimension |n|+r-3. There are forgetful maps W_n→ 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
more » ... ndix, we work out the 2- and 3-dimensional associahedra in detail.
doi:10.2140/agt.2019.19.743 fatcat:hvfs2y5gqbc7zdlsq6ogz4urqi