Volume 19, issue 2 (2019)

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Nathaniel Bottman

Algebraic & Geometric Topology 19 (2019) 743–806

For any r 1 and n 0r {0} we construct a poset Wn 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 Ŵn is an abstract polytope of dimension |n| + r 3. There are forgetful maps Wn Kr, where Kr is the (r2)–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 2–associahedra in detail.

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polytopes, associahedra, Fukaya category, pseudoholomorphic quilts
Mathematical Subject Classification 2010
Primary: 53D37
Received: 3 September 2017
Revised: 19 June 2018
Accepted: 20 August 2018
Published: 12 March 2019
Nathaniel Bottman
School of Mathematics
Institute for Advanced Study
Princeton, NJ
United States