Arboreal singularities

Nadler, David

doi:10.2140/gt.2017.21.1231

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Arboreal singularities

David Nadler

Geometry & Topology 21 (2017) 1231–1274

DOI: 10.2140/gt.2017.21.1231

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.

Keywords

Lagrangian singularities, microlocal sheaves

Mathematical Subject Classification 2010

Primary: 32S05, 53D37

References

Publication

Received: 30 October 2015

Revised: 6 March 2016

Accepted: 23 April 2016

Published: 17 March 2017

Proposed: Yasha Eliashberg

Seconded: Leonid Polterovich, Ciprian Manolescu

Authors

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

Volume 21, issue 2 (2017)