Geodesic
2–associahedra
Bottman, Nathaniel1
1 School of Mathematics, Institute for Advanced Study, Princeton, NJ, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 2, pp. 743-806

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

For any r ≥ 1 and n ∈ ℤ≥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 (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 2–associahedra in detail.

DOI : 10.2140/agt.2019.19.743
Classification : 53D37
Keywords: polytopes, associahedra, Fukaya category, pseudoholomorphic quilts

Bottman, Nathaniel 1

1 School of Mathematics, Institute for Advanced Study, Princeton, NJ, United States 
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Bottman, Nathaniel. 2–associahedra. Algebraic and Geometric Topology, Tome 19 (2019) no. 2, pp. 743-806. doi: 10.2140/agt.2019.19.743

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