2006/08/18 by Jae-Wook Chung, Xiao-Song Lin, Chung, Jae-Wook +1 · 1 citation
Computer Science · Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0608459
openalex publication_date 2006/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a chain homotopy invariant on the collection of all quasi-isomorphisms from a based chain complex to another. It shares nice properties with torsion of acyclic based chain complexes, like multiplicativity and duality. We will further generalize our torsion to quasi-isomorphisms between free chain complexes over a ring under some mild condition. We anticipate that the study of torsion of quasi-isomorphisms will be fruitful in many directions, and in particular, in the study of links in 3-manifolds.