Alexander invariants and cohomology jump loci in group extensions
نویسندگان
چکیده
منابع مشابه
Fundamental groups, Alexander invariants, and cohomology jumping loci
We survey the cohomology jumping loci and the Alexander-type invariants associated to a space, or to its fundamental group. Though most of the material is expository, we provide new examples and applications, which in turn raise several questions and conjectures. The jump loci of a space X come in two basic flavors: the characteristic varieties, or, the support loci for homology with coefficien...
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Introduction. Let G be a group, K an invariant subgroup of G. The purpose of this paper is to investigate the relations between the cohomology groups of G, K, and G/K. As in the case of fibre spaces, it turns out that such relations can be expressed by a spectral sequence whose term E2 is HiG/K, HiK)) and whose term Em is the graduated group associated with i7(G). This problem was first studied...
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Quadratic forms q(x1, . . . , xn) over a field k are the classical examples of nonlinear scalar-valued functions on a vector space V = k, and they lie at the foundation of nineteenth-century analytic geometry. Motivated by problems such as finding the axes of a conic, geometers studied quadratic forms under symmetries of V . Given two quadratic forms q, q′ on V , how may we tell if q and q′ are...
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ژورنال
عنوان ژورنال: Annali della Scuola normale superiore di Pisa. Classe di scienze
سال: 2022
ISSN: ['0391-173X', '2036-2145']
DOI: https://doi.org/10.2422/2036-2145.202112_005