Constructible Sheaves and the Fukaya Category
| dc.creator | Nadler, David | |
| dc.creator | Zaslow, Eric | |
| dc.date | 2006-04-18 | |
| dc.date | 2008-06-16 | |
| dc.date.accessioned | 2026-07-07T09:44:35Z | |
| dc.date.available | 2026-07-07T09:44:35Z | |
| dc.description | Let $X$ be a compact real analytic manifold, and let $T^*X$ be its cotangent bundle. Let $Sh(X)$ be the triangulated dg category of bounded, constructible complexes of sheaves on $X$. In this paper, we develop a Fukaya $A_\infty$-category $Fuk(T^*X)$ whose objects are exact, not necessarily compact Lagrangian branes in the cotangent bundle. We write $Tw Fuk(T^*X)$ for the $A_\infty$-triangulated envelope of $Fuk(T^*X)$ consisting of twisted complexes of Lagrangian branes. Our main result is that $Sh(X)$ quasi-embeds into $Tw Fuk(T^*X)$ as an $A_\infty$-category. Taking cohomology gives an embedding of the corresponding derived categories. | |
| dc.description | 56 pages; to appear in JAMS | |
| dc.identifier | https://arxiv.org/abs/math/0604379 | |
| dc.identifier | http://arxiv.org/abs/math/0604379 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162925 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | Representation Theory | |
| dc.title | Constructible Sheaves and the Fukaya Category | |
| dc.type | text |