منابع مشابه
New Permutation Representations of The Braid Group
We give a new infinite family of group homomorphisms from the braid group Bk to the symmetric group Smk for all k and m ≥ 2. Most known permutation representations of braids are included in this family. We prove that the homomorphisms in this family are non-cyclic and transitive. For any divisor l of m, 1 ≤ l < m, we prove in particular that if m l is odd then there are 1+ m l non-conjugate hom...
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Drinfel’d used associators to construct families of universal representations of braid groups. We consider semi-associators (i.e., we drop the pentagonal axiom and impose a normalization in degree one). We show that the process may be reversed, to obtain semi-associators from universal representations of 3–braids. We view braid groups as subgroups of braid-permutation groups. We construct a fam...
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We say that a permutation π is merged from permutations ρ and τ , if we can color the elements of π red and blue so that the red elements are order-isomorphic to ρ and the blue ones to τ . A permutation class is a set of permutations closed under taking subpermutations. A permutation class C is splittable if it has two proper subclasses A and B such that every element of C can be obtained by me...
متن کاملThe singularity obstruction for group splittings
We study an obstruction to splitting a finitely generated group G as an amalagamated free product or HNN extension over a given subgroup H and show that when the obstruction is “small” G splits over a related subgroup. Applications are given which generalise decomposition theorems from low dimensional topology.
متن کاملGeometric 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...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2003
ISSN: 0304-9914
DOI: 10.4134/jkms.2003.40.2.179