منابع مشابه
Pure Braid Subgroups of Braided Thompson’s Groups
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 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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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 classify the (finite and infinite) virtually cyclic subgroups of the pure braid groups PnpRP2q of the projective plane. The maximal finite subgroups of PnpRP2q are isomorphic to the quaternion group of order 8 if n 3, and to Z4 if n ¥ 4. Further, for all n ¥ 3, up to isomorphism, the following groups are the infinite virtually cyclic subgroups of PnpRP2q: Z, Z2 Z and the amalgamated product ...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2001
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2001.134196