## Geometry & Topology

### Arboreal singularities

#### Abstract

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

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

Dates
Revised: 6 March 2016
Accepted: 23 April 2016
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510859178

Digital Object Identifier
doi:10.2140/gt.2017.21.1231

Mathematical Reviews number (MathSciNet)
MR3626601

Zentralblatt MATH identifier
06701806

#### Citation

Nadler, David. Arboreal singularities. Geom. Topol. 21 (2017), no. 2, 1231--1274. doi:10.2140/gt.2017.21.1231. https://projecteuclid.org/euclid.gt/1510859178

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