2005/10/27 by Bogdan Ichim, Udo Vetter
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AC
paper · pdf · doi:10.1080/00927870600876284
published as Communications in Algebra 34, 4131 - 4156 (2006)
arxiv created 2005/10/27 · openalex publication_date 2006/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We describe Koszul type complexes associated with a linear map from any module to a free module, and vice versa with a linear map from a free module to an arbitrary module, generalizing the classical Koszul complexes. Given a short complex of finite free modules, we assemble these complexes to what we call Koszul bicomplexes. They are used in order to investigate the homology of the Koszul complexes in projective dimension one. As in the case of the classical Koszul complexes, this homology turns out to be grade sensitive. In a special setup, we obtain necessary conditions for a map of free modules to be lengthened to a short complex of free modules.