Torsion of Quasi-Isomorphisms

Jae-Wook Chung; Xiao-Song Lin

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Torsion of Quasi-Isomorphisms

Jae-Wook Chung·Xiao-Song Lin

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Abstract

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.

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BibTeX RIS

Jae-Wook Chung, Xiao-Song Lin. 2006-08-29. Torsion of Quasi-Isomorphisms. https://arxiv.org/abs/math/0608459

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