Arboreal singularities

Nadler, David¹

¹ Department of Mathematics, University of California, Berkeley, Evans Hall, Berkeley, CA 94720-3840, United States

Geometry & topology, Tome 21 (2017) no. 2, pp. 1231-1274.

Résumé

We introduce a class of combinatorial singularities of Lagrangian skeleta of symplectic manifolds. The link of each singularity is a finite regular cell complex homotopy equivalent to a bouquet of spheres. It is determined by its face poset, which is naturally constructed starting from a tree (nonempty finite acyclic graph). The choice of a root vertex of the tree leads to a natural front projection of the singularity along with an orientation of the edges of the tree. Microlocal sheaves along the singularity, calculated via the front projection, are equivalent to modules over the quiver given by the directed tree.

Détail

DOI : 10.2140/gt.2017.21.1231

Classification : 32S05, 53D37
Keywords: Lagrangian singularities, microlocal sheaves

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