A New Zeta Function, Natural for Links

R. F. Williams

Chapter 27 in From Topology to Computation: Proceedings of the Smalefest, 1993, pp 270-278 from Springer

Abstract: Abstract We overcome a former frustration: A new “determinant” is defined, not requiring completely abelian matrix entries. In fact, non-abelian invariants do occur in dynamical systems, so that the usual determinant is not available. This “link-determinant” is invariant only under the group of permutations, not the general linear group. But permutations are the only pertinent transformations in the setting of symbolic dynamics. That is to say, permuting the elements of a Markov matrix makes sense; linear combinations of them do not. For our immediate purpose, keeping track of knots and links via their fundamental group words, the zeta function defined in terms of this new determinant seems ideal.

Keywords: Periodic Orbit; Zeta Function; Homoclinic Orbit; Cyclic Permutation; General Linear Group (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1007/978-1-4612-2740-3_27

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