2021/12/05 by Adam Brown, Brown, Adam, Ondřej Draganov +1
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2112.02609
openalex publication_date 2021/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce two new methods for constructing injective resolutions of sheaves of finite-dimensional vector spaces on finite posets. Our main result is the existence and uniqueness of a minimal injective resolution of a given sheaf and an algorithm for its construction. For the constant sheaf on a simplicial complex, we give a topological interpretation of the multiplicities of indecomposable injective sheaves in the minimal injective resolution, and give asymptotically tight bounds on the complexity of computing the minimal injective resolution with our algorithm.