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Algebraic torsion, zeta function and Dirichlet series for graph links in homology 3-spheres

Published online by Cambridge University Press:  19 September 2008

András Némethi
András Némethi
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio, 43210-1174, USA
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Abstract

In this paper, we define the algebraic torsion τ associated with an -constructible sheaf ℱ on a topological space X and a ring homomorphism π1(X) → Z (with an acyclicity condition). If (X, ) has a fiber structure over S1, then τ is equal to the zeta function of the monodromy acting on the hypercohomology of the fiber. If X is the complement of a link in a homology 3-sphere and is given by a link such that admits a fiberable splice diagram, then this zeta function has a product decomposition (corresponding to the Jaco-Shalen-Johansson decomposition). This can be interpreted as a ‘Lefschetz type formula’ for a dynamical system suitably chosen.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 1 , March 1993 , pp. 131 - 142
Copyright
Copyright © Cambridge University Press 1993

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