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Arboreal singularities

David Nadler

Geometry & Topology 21 (2017) 1231–1274

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.

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Lagrangian singularities, microlocal sheaves
Mathematical Subject Classification 2010
Primary: 32S05, 53D37
Received: 30 October 2015
Revised: 6 March 2016
Accepted: 23 April 2016
Published: 17 March 2017
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Ciprian Manolescu
David Nadler
Department of Mathematics
University of California, Berkeley
Evans Hall
Berkeley, CA 94720-3840
United States