GEOMETRIC PRESENTATIONS FOR THE PURE BRAID GROUP
نویسندگان
چکیده
منابع مشابه
Geometric Presentations for the Pure Braid Group
We give several new positive finite presentations for the pure braid group that are easy to remember and simple in form. All of our presentations involve a metric on the punctured disc so that the punctures are arranged “convexly”, which is why we describe them as geometric presentations. Motivated by a presentation for the full braid group that we call the “rotation presentation”, we introduce...
متن کاملThe Chen Groups of the Pure Braid Group
A b st r ac t . The Chen groups of a group are the lower central series quotients of its maximal metabelian quotient. We show that the Chen groups of the pure braid group Pn are free abelian, and we compute their ranks. The computation of these Chen groups reduces to the computation of the Hilbert series of a certain graded module over a polynomial ring, and the latter is carried out by means o...
متن کاملThe Chen Groups of the Pure Braid Group DANIEL
The Chen groups of a group are the lower central series quotients of its maximal metabelian quotient. We show that the Chen groups of the pure braid group Pn are free abelian, and we compute their ranks. The computation of these Chen groups reduces to the computation of the Hilbert series of a certain graded module over a polynomial ring, and the latter is carried out by means of a Groebner bas...
متن کاملTwo-generator Subgroups of the Pure Braid Group
We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2009
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216509006859