منابع مشابه
Alexander Modules of Irreducible C-groups
A complete description of the Alexander modules of knotted n-manifolds in the sphere S n+2 , n ≥ 2, and irreducible Hurwitz curves is given. This description is applied to investigate properties of the first homology groups of cyclic coverings of the sphere S n+2 and the projective complex plane CP 2 branched respectively alone knotted n-manifolds and along irreducible Hurwitz (in particular, a...
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We will discuss a technique to distinguish knots via an algebraic invariant, namely the Alexander module, which is a module associated to the universal abelian cover of the complement of a knot. We will present a generalization of the Alexander module by constructing modules corresponding to different regular covering spaces of the knot complement. We will present a numerical invariant that can...
متن کاملIntersection Homology and Alexander Modules of Hypersurface Complements
Let V be a degree d, reduced hypersurface in CP, n ≥ 1, and fix a generic hyperplane, H. Denote by U the (affine) hypersurface complement, CP−V ∪H, and let U be the infinite cyclic covering of U corresponding to the kernel of the linking number homomorphism. Using intersection homology theory, we give a new construction of the Alexander modules Hi(U ;Q) of the hypersurface complement and show t...
متن کاملR-MODULES FOR THE ALEXANDER COHOMOLOGY THEORY APPROVED: Major Professor
The Alexander Wallace Spanier cohomology theory associates with an arbitrary topological space an abelian group. In this paper, an arbitrary topological space is associated with an R-module. The construction of the R-module is similar to the Alexander Wallace Spanier construction of the abelian group. In Chapter I, the algebraic and topological material necessary to construct the theor'y is lis...
متن کاملStanley Decompositions of Squarefree Modules and Alexander Duality
In this paper we study how prime filtrations and squarefree Stanley decompositions of squarefree modules over the polynomial ring and the exterior algebra behave with respect to Alexander duality.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1984
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1984-0735584-8