Microlocal branes are constructible sheaves
| dc.creator | Nadler, David | |
| dc.date | 2006-12-14 | |
| dc.date | 2009-02-12 | |
| dc.date.accessioned | 2026-07-07T12:40:45Z | |
| dc.date.available | 2026-07-07T12:40:45Z | |
| dc.description | Let $X$ be a real analytic manifold, and let $T^*X$ be its cotangent bundle. In a recent paper with E. Zaslow \cite{NZ}, we showed that the dg category $Sh_c(X)$ of constructible sheaves on $X$ quasi-embeds into the triangulated envelope $F(T^*X)$ of the Fukaya category of $T^*X$. We prove here that the quasi-embedding is in fact a quasi-equivalence. When $X$ is complex, one may interpret this as a topological analogue of the identification of Lagrangian branes in $T^*X$ and holonomic $D_X$-modules developed by Kapustin and Kapustin-Witten from a physical perspective. As a concrete application, we show that compact connected exact Lagrangians in $T^*X$ (with some modest homological assumptions) are equivalent in the Fukaya category to the zero section. In particular, this determines their (complex) cohomology ring and homology class in $T^*X$, and provides a homological bound on their number of intersection points. An independent characterization of compact branes in $T^*X$ has recently been obtained by Fukaya-Seidel-Smith. | |
| dc.description | 49 pages; minor expository changes | |
| dc.identifier | https://arxiv.org/abs/math/0612399 | |
| dc.identifier | http://arxiv.org/abs/math/0612399 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219542 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Representation Theory | |
| dc.title | Microlocal branes are constructible sheaves | |
| dc.type | text |