Homology, lower central series, and hyperplane arrangements
نویسندگان
چکیده
منابع مشابه
Lower Central Series and Free Resolutions of Hyperplane Arrangements
If M is the complement of a hyperplane arrangement, and A = H(M, k) is the cohomology ring of M over a field of characteristic 0, then the ranks, φk, of the lower central series quotients of π1(M) can be computed from the Betti numbers, bii = dimTor A i (k, k)i, of the linear strand in a minimal free resolution of k over A. We use the Cartan-Eilenberg change of rings spectral sequence to relate...
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The quotients Gk/Gk+1 of the lower central series of a finitely presented group G are an important invariant of this group. In this work we investigate the ranks of these quotients in the case of a certain class of conjugation-free groups, which are groups generated by x1, . . . , xn and having only cyclic relations: xitxit−1 · . . . · xi1 = xit−1 · . . . · xi1xit = · · · = xi1xit · . . . · xi2...
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As is well-known, the homology groups of the complement of a complex hyperplane arrangement are torsion-free. Nevertheless, as we showed in a recent paper [2], the homology groups of the Milnor fiber of such an arrangement can have non-trivial integer torsion. We give here a brief account of the techniques that go into proving this result, outline some of its applications, and indicate some fur...
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ژورنال
عنوان ژورنال: European Journal of Mathematics
سال: 2019
ISSN: 2199-675X,2199-6768
DOI: 10.1007/s40879-019-00392-x