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.
 Publication:

arXiv eprints
 Pub Date:
 September 2013
 DOI:
 10.48550/arXiv.1309.4122
 arXiv:
 arXiv:1309.4122
 Bibcode:
 2013arXiv1309.4122N
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Combinatorics;
 Mathematics  Representation Theory
 EPrint:
 32 pages