Sheaves on Triangulated Spaces and Koszul Duality
| dc.creator | Vybornov, Maxim | |
| dc.date | 1999-10-27 | |
| dc.date | 2000-10-15 | |
| dc.date.accessioned | 2026-07-07T05:31:18Z | |
| dc.date.available | 2026-07-07T05:31:18Z | |
| dc.description | Let $X$ be a finite connected simplicial complex, and let $δ$ be a perversity (i.e., some function from integers to integers). One can consider two categories: (1) the category of perverse sheaves cohomologically constructible with respect to the triangulation, and (2) the category of sheaves constant along the perverse simplices ($δ$-sheaves). We interpret the categories (1) and (2) as categories of modules over certain quadratic (and even Koszul) algebras $A(X,δ)$ and $B(X,δ)$ respectively, and we prove that $A(X,δ)$ and $B(X,δ)$ are Koszul dual to each other. We define the $δ$-perverse topology on $X$ and prove that the category of sheaves on perverse topology is equivalent to the category of $δ$ sheaves. Finally, we study the relationship between the Koszul duality functor and the Verdier duality functor for simplicial sheaves and cosheaves. | |
| dc.description | 41 page, AMSTEX. Minor improvements, new section 4.2.12 | |
| dc.identifier | https://arxiv.org/abs/math/9910150 | |
| dc.identifier | http://arxiv.org/abs/math/9910150 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79294 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Algebraic Geometry | |
| dc.title | Sheaves on Triangulated Spaces and Koszul Duality | |
| dc.type | text |