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- Title
Alexander Polynomials: Essential Variables and Multiplicities.
- Authors
Dimca, Alexandru; Papadima, Stefan; Suciu, Alexander I.
- Abstract
We explore the codimension-one strata in the degree-one cohomology jumping loci of a finitely generated group, through the prism of the multivariable Alexander polynomial. As an application, we give new criteria that must be satisfied by fundamental groups of smooth, quasi-projective complex varieties. These criteria establish precisely which fundamental groups of boundary manifolds of complex line arrangements are quasi-projective. We also give sharp upper bounds for the twisted Betti ranks of a group, in terms of multiplicities constructed from the Alexander polynomial. For Seifert links in homology 3-spheres, these bounds become equalities, and our formula shows explicitly how the Alexander polynomial determines all the characteristic varieties.
- Subjects
OPERATIONS (Algebraic topology); HOMOLOGY theory; POLYNOMIALS; MANIFOLDS (Mathematics); BOUNDARY value problems; MULTIPLICITY (Mathematics)
- Publication
IMRN: International Mathematics Research Notices, 2008, Vol 2008, p1
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnm119