共查询到20条相似文献,搜索用时 12 毫秒
1.
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. 相似文献
2.
D.L. Gonçalves 《Journal of Pure and Applied Algebra》2003,182(1):33-64
We describe some of the properties of the pure braid groups of surfaces different from and . In the case of compact, connected, orientable surfaces without boundary and of genus at least two, we give a necessary and sufficient condition for the splitting of the pure braid group exact sequence of Fadell and Neuwirth, thus answering completely a question of Birman. 相似文献
3.
D.L. Gonçalves 《Journal of Pure and Applied Algebra》2004,186(2):187-218
We describe some of the properties of the pure braid groups of surfaces different from and . In the case of compact, connected, orientable surfaces without boundary and of genus at least two, we give a necessary and sufficient condition for the splitting of the pure braid group exact sequence of Fadell and Neuwirth, thus answering completely a question of Birman. 相似文献
4.
We show how the finite symplectic groups arise as quotients of the pure symplectic braid group. Via [SV] certain of these
groups — in particular, all groups Sp
n
(2) — occur as Galois groups over ℚ.
Supported by NSF grant DMS-9306479. 相似文献
5.
Dmitri G. Markushevich 《Geometriae Dedicata》1991,40(1):73-96
A corepresentation for the generalized pure braid group ID
n of the Coxeter group D
n is constructed. The lower central series of ID
n is investigated. It is proved that ID
n is approximable by torsion-free nilpotent groups, so R. Hain's obstruction to the solvability of the generalized Riemann-Hilbert problem is trivial for ID
n. 相似文献
6.
Raul Cordovil Antnio Guedes de Oliveira Michel Las Vergnas 《Discrete Mathematics》1996,160(1-3):105-113
In this paper, a configuration with n = (2d) points in the plane is described. This configuration, as a matroid, is a Desargues configuration if d = 5, and the union of (5d) such configurations if d> 5. As an oriented matroid, it is a rank 3 truncation of the directed complete graph on d vertices. From this fact, it follows from a version of the Lefschetz-Zariski theorem implied by results of Salvetti that the fundamental group π of the complexification of its line arrangement is Artin's pure (or coloured) braid group on d strands.
In this paper we obtain, by using techniques introduced by Salvetti, a new algorithm for finding a presentation of π based on this particular configuration. 相似文献
7.
Peter Lee 《Selecta Mathematica, New Series》2013,19(2):461-508
If an augmented algebra $K$ over $\mathbb Q $ is filtered by powers of its augmentation ideal $I$ , the associated graded algebra $gr_I K$ need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper, we give a sufficient criterion (called the PVH Criterion) for $gr_I K$ to be quadratic. When $K$ is the group algebra of a group $G$ , quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for $G$ . Thus, the PVH Criterion also implies the existence of such a universal finite type invariant for the group $G$ . We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a universal finite type invariant. 相似文献
8.
Muhammad A. Albar 《代数通讯》2013,41(23):2977-2984
9.
10.
Stephen P. Humphries 《Israel Journal of Mathematics》2004,143(1):189-222
We prove that (with two possible exceptions) the Hurwitz braid group action on the sequence of standard generators of an irreducible
Artin group has a finite orbit if and only if the Artin group is of finite type (i.e., the corresponding Coxeter group is
finite). 相似文献
11.
Daan Krammer 《Transactions of the American Mathematical Society》2008,360(8):4029-4061
We construct a class of Garside groupoid structures on the pure braid groups, one for each function (called labelling) from the punctures to the integers greater than 1. The object set of the groupoid is the set of ball decompositions of the punctured disk; the labels are the perimeters of the regions. Our construction generalises Garside's original Garside structure, but not the one by Birman-Ko-Lee. As a consequence, we generalise the Tamari lattice ordering on the set of vertices of the associahedron.
12.
Mohammad N. Abdulrahim 《Proceedings of the American Mathematical Society》1997,125(5):1249-1257
This work is directed towards the open question of the faithfulness of the reduced Gassner representation of the pure braid group, . Long and Paton proved that if a Burau matrix has ones on the diagonal and zeros below the diagonal then is the identity matrix. In this paper, a generalization of Long and Paton's result will be proved. Our main theorem is that if the trace of the image of an element of under the reduced Gassner representation is , then this element lies in the kernel of this representation. Then, as a corollary, we prove that an analogue of the main theorem holds true for the Burau representation of the braid group.
13.
Mohammad N. Abdulrahim 《Proceedings of the American Mathematical Society》1997,125(6):1617-1624
We will give a necessary and sufficient condition for the specialization of the reduced Gassner representation to be irreducible. It will be shown that for , is irreducible if and only if .
14.
Daan Krammer 《Inventiones Mathematicae》2000,142(3):451-486
We study a linear representation ρ:B
n
? GL
m
(Z[q
±1,t
±1]) with m=n(n-1)/2. We will show that for n=4, this representation is faithful. We prove a relation with the new Charney length function. We formulate a conjecture implying
that ρ is faithful for all n.
Oblatum 15-VI-1999 & 24-II-2000?Published online: 18 September 2000 相似文献
15.
The quaternion group as a subgroup of the sphere braid groups 总被引:1,自引:0,他引:1
Let n 3. We prove that the quaternion group of order 8 is realisedas a subgroup of the sphere braid group Bn(2) if and only ifn is even. If n is divisible by 4, then the commutator subgroupof Bn(2) contains such a subgroup. Further, for all n 3, Bn(2)contains a subgroup isomorphic to the dicyclic group of order4n. 相似文献
16.
17.
Betty Jane Gassner 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1961,25(1-2):10-22
A dissertation in the Department of Mathematics submitted to the Faculty of the Graduate School of Arts and Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy at New York University. 相似文献
18.
In this article we prove a special case of a conjecture of A. Abrams and R. Ghrist about fundamental groups of certain aspherical spaces. Specifically, we show that the \(n\) -point braid group of a linear tree is a right-angled Artin group for each \(n\) . 相似文献
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