A conjugation-free geometric presentation of fundamental groups of arrangements
نویسندگان
چکیده
منابع مشابه
A Conjugation-Free Geometric Presentation of Fundamental Groups of Arrangements II: Expansion and Some Properties
A conjugation-free geometric presentation of a fundamental group is a presentation with the natural topological generators x1, . . . , xn and the cyclic relations: xikxik−1 · · ·xi1 = xik−1 · · ·xi1xik = · · · = xi1xik · · ·xi2 with no conjugations on the generators. We have already proved in [13] that if the graph of the arrangement is a disjoint union of cycles, then its fundamental group has...
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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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Abstract. Continuing our work on the fundamental groups of conic-line arrangements [3], we obtain presentations of fundamental groups of the complements of three families of quadric arrangements in P. The first arrangement is a union of n conics, which are tangent to each other at two common points. The second arrangement is composed of n quadrics which are tangent to each other at one common p...
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2010
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-010-0380-2