. A T ] 2 9 A ug 2 00 6 TORSION OF QUASI - ISOMORPHISMS
نویسندگان
چکیده
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.
منابع مشابه
1 8 A ug 2 00 6 TORSION OF QUASI - ISOMORPHISMS
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 bas...
متن کاملar X iv : h ep - t h / 06 08 05 6 v 1 8 A ug 2 00 6 hep - th / 0608056 Derived categories and stacks in physics
This is a summary of a talk given at the Vienna homological mirror symmetry conference in June 2006. We review how both derived categories and stacks enter physics. In both cases, equivalences are realized via renormalization group flow: in the case of derived categories, (boundary) renormalization group flow realizes the mathematical procedure of localization on quasi-isomorphisms, and in the ...
متن کامل2 9 A ug 2 00 6 THE OUTER SPACE OF A FREE PRODUCT
We associate a contractible “outer space” to any free product of groups G = G1 ∗ · · · ∗ Gq. It equals Culler-Vogtmann space when G is free, McCulloughMiller space when no Gi is Z. Our proof of contractibility (given when G is not free) is based on Skora’s idea of deforming morphisms between trees. Using the action of Out(G) on this space, we show that Out(G) has finite virtual cohomological di...
متن کامل2 00 9 Introduction to the log minimal model program for log canonical pairs
We describe the foundation of the log minimal model program for log canonical pairs according to Ambro’s idea. We generalize Kollár’s vanishing and torsion-free theorems for embedded simple normal crossing pairs. Then we prove the cone and contraction theorems for quasi-log varieties, especially, for log canonical pairs.
متن کامل