Fundamental Groups of Real Arrangements and Torsion in the Lower Central Series Quotients
نویسندگان
چکیده
منابع مشابه
Conjugation-free Groups, Lower Central Series and Line Arrangements
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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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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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2018
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2018.1428131