Two-generator subgroups of the pure braid group
نویسندگان
چکیده
منابع مشابه
Two-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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We describe pure braided versions of Thompson’s group F . These groups, BF and B̂F , are subgroups of the braided versions of Thompson’s group V , introduced by Brin and Dehornoy. Unlike V , elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe i...
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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...
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We show that two knots have matching Vassiliev invariants of order less than n if and only if they are equivalent modulo the nth group of the lower central series of some pure braid group, thus characterizing Vassiliev’s knot invariants in terms of the structure of the braid groups. We also prove some results about knots modulo the nth derived subgroups of the pure braid groups, and about knots...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2009
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-009-9440-8