Geometry & Topology

Arboreal singularities

David Nadler

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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.

Article information

Geom. Topol., Volume 21, Number 2 (2017), 1231-1274.

Received: 30 October 2015
Revised: 6 March 2016
Accepted: 23 April 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32S05: Local singularities [See also 14J17] 53D37: Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33]

Lagrangian singularities microlocal sheaves


Nadler, David. Arboreal singularities. Geom. Topol. 21 (2017), no. 2, 1231--1274. doi:10.2140/gt.2017.21.1231.

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