TWISTED ALEXANDER INVARIANTS, REIDEMEISTER TORSION, AND CASSON–GORDON INVARIANTS
نویسندگان
چکیده
منابع مشابه
Refinement of Twisted Alexander Invariants and Sign-determined Reidemeister Torsions
Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method. We can show that the refined invariants coincide with sign-determined Reidemeister torsions associated to some Euler structures. As an application, we obtain stronger necessary conditions for a knot to be fibered than those previously know...
متن کاملNormalization of Twisted Alexander Invariants
Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants. We can show that the invariants coincide with signdetermined Reidemeister torsion in a normalized setting and refine the duality theorem. As an application, we obtain stronger necessary co...
متن کاملDynamics of Twisted Alexander Invariants
The Pontryagin dual of the twisted Alexander module for a dcomponent link and GLNZ representation is an algebraic dynamical system with an elementary description in terms of colorings of a diagram. In the case of a knot, its associated topological entropy is the logarithmic growth rate of the number of torsion elements in the twisted first-homology group of r-fold cyclic covers of the knot comp...
متن کاملTwisted Alexander Invariants of Twisted Links
Let L = 1∪· · ·∪ d+1 be an oriented link in S3, and let L(q) be the d-component link 1 ∪· · ·∪ d regarded in the homology 3-sphere that results from performing 1/q-surgery on d+1. Results about the Alexander polynomial and twisted Alexander polynomials of L(q) corresponding to finite-image representations are obtained. The behavior of the invariants as q increases without bound is described.
متن کاملFibred Knots and Twisted Alexander Invariants
We study the twisted Alexander invariants of fibred knots. We establish necessary conditions on the twisted Alexander invariants for a knot to be fibred, and develop a practical method to compute the twisted Alexander invariants from the homotopy type of a monodromy. It is illustrated that the twisted Alexander invariants carry more information on fibredness than the classical Alexander invaria...
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ژورنال
عنوان ژورنال: Topology
سال: 1999
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(98)00039-1