Alexander Ideals of Links

Hillman, Jonathan A.

doi:10.1007/bfb0091682

Cited by 76 publications

(44 citation statements)

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“…Since the signature jump function is invariant under link concordance [4], it is expected that signatures can be calculated from Seifert matrices and patterns. Second, since the Blanchfield form is determined by a Seifert matrix [15,12,8] and the Blanchfield form of a covering link of a link L is the image of the Blanchfield form of L under a transfer homomorphism [7,8], it is expected that a Seifert matrix of a covering link of L can also be obtained from a Seifert matrix of L. In this sense, our formula for Seifert matrices is analogous to the transfer homomorphism for Blanchfield forms. We remark that no explicit formula for the latter is known.…”

Section: Seifert Matrices Of Covering Linksmentioning

confidence: 98%

Signature invariants of covering links

Choon

2005

Trans. Amer. Math. Soc.

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Abstract. We apply the theory of signature invariants of links in rational homology spheres to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, we derive an explicit formula to compute signature invariants of their covering links. Using the formula, we produce fused boundary links that are positive mutants of ribbon links but are not concordant to boundary links. We also show that for any finite collection of patterns, there are homology boundary links that are not concordant to any homology boundary links admitting a pattern in the collection.

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Section: Seifert Matrices Of Covering Linksmentioning

confidence: 98%

Signature invariants of covering links

Choon

2005

Trans. Amer. Math. Soc.

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“…Some answers to this question can be given as follows. The cohomology modules may be related to the homology modules by the Universal Coefficient spectral sequence (see [30], p.20 or [31], Thm. 2.3):…”

Section: Homology Versus Cohomology Alexander Modulesmentioning

confidence: 99%

On the Alexander invariants of hypersurface complements

Maxim

2007

Singularity Theory

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Abstract. We start with a discussion on Alexander invariants, and then prove some general results concerning the divisibility of the Alexander polynomials and the supports of the Alexander modules, via Artin's vanishing theorem for perverse sheaves. We conclude with explicit computations of twisted cohomology following an idea already exploited in the hyperplane arrangement case, which combines the degeneration of the Hodge to de Rham spectral sequence with the purity of some cohomology groups.

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“…Rappelons la définition des idéaux de Fitting (consulter [7], chapter 3). Si M possède une présentation…”

Section: Comparaison Desunclassified

“…Il est bien connu que cet idéal ne dépend pas de la présentation choisie, mais uniquement de M (voir [7] et références). Notons maintenant ∆ k (M ) un pgcd deséléments de E k (M ).…”

Section: Comparaison Desunclassified

K_2 et conjecture de Greenberg dans les \mathbb{Z}_p-extensions multiples

Quang¹,

Vauclair²

2005

J. Théor. Nombres Bordeaux

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Alexander Ideals of Links

Cited by 76 publications

References 0 publications

Signature invariants of covering links

Signature invariants of covering links

On the Alexander invariants of hypersurface complements

K_2 et conjecture de Greenberg dans les \mathbb{Z}_p-extensions multiples

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