The Determinantal Ideals of Link Modules. I
نویسنده
چکیده
of ZfiΓ-modules and ZH-homomorphisms will be called an augmentation sequence if A is a finitely generated Ziϊ-module. Since ZH is a noetherian ring, A is then a finitely presented Zff-module; also, the module B in an augmentation sequence is finitely presented, since it is isomorphic to a submodule of A. For instance, if L £ S is a tame link of m components, G = π^S — L), and G is the commutator subgroup of G, then G/G' s H. lί p: X ~> X ~ S — L is the universal abelian cover of X, and JP is its fiber, then as discussed in [1, pp. 227-234] there is an augmentation sequence (1) in which B = H^X; Z) is the Alexander invariant of L and A = H^X, F; Z) is the Alexander module of L. These abelian groups are iϊ-modules under the action given by identifying H ~ (?/(?' with the group of covering automorphisms of X. Given an augmentation sequence (1), determinantal ideals Ek(A) and Ek(B) can be defined for any keZ (see § 2); this paper is con-
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