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1.
N. S. Markaryan 《Mathematical Notes》1996,59(6):611-617
In the paper, the homology of the braid groups with twisted coefficients and the homology of commutator subgroups of the braid
groups are calculated. The main tool is the multiplicative structure on the homology induced by the “addition” of braid groups.
Translated fromMatematicheskie Zametki, Vol. 59, No. 6, pp. 846–854, June, 1996.
This research was partially supported by the International Science Foundation under grant MQO000. 相似文献
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We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the -norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings of and for all . As a consequence we are also able to embed a variety of Gromov hyperbolic groups quasi-isometrically in pure braid groups and in the group . Examples include hyperbolic surface groups, some HNN-extensions of these along cyclic subgroups and the fundamental group of a certain closed hyperbolic 3-manifold.
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We prove two theorems linking the cohomology of a pro- group with the conjugacy classes of its finite subgroups.
The number of conjugacy classes of elementary abelian -subgroups of is finite if and only if the ring is finitely generated modulo nilpotent elements.
If the ring is finitely generated, then the number of conjugacy classes of finite subgroups of is finite.
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Let X be a topological space upon which a compact connected Lie group G acts. It is well known that the equivariant cohomology H * G (X; Q) is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology H * T (X; Q), where T is a maximal torus of G. This relationship breaks down for coefficient rings k other than Q. Instead, we prove that under a mild condition on k the algebra H * G (X; k) is isomorphic to the subalgebra of H * T (X; k) annihilated by the divided difference operators. 相似文献
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Let G be a discrete group generated by reflections in hyperbolic or Euclidean space, and let H G be a finite index reflection subgroup. Suppose that the fundamental chamber of G is a finite volume polytope with k facets. We prove that the fundamental chamber of H has at least k facets.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 90–92, 2004Original Russian Text Copyright © by A. A. Felikson and P. V. Tumarkin 相似文献
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We derive the classification of finite Coxeter groups in a purely algebraic manner from a simple result concerning involutions and a result of Dyer on reflection subgroups, for which we give a very short proof. 相似文献
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Panagiotis Soules 《Archiv der Mathematik》2003,80(5):449-457
For soluble groups, the Fitting length is bounded by a function of the maximum order
of the Fitting subgroups of 2-generator subgroups. 相似文献
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Muhammad A. Albar 《代数通讯》2013,41(23):2977-2984
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Based on a graph-theoretic analysis, we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m, p, n), and describe the irreducible subsystems of all possible types in the root system R(m, p, n) of G(m, p, n). 相似文献
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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. 相似文献
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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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Yu. A. Mikhalchishina 《Siberian Mathematical Journal》2013,54(4):666-678
We study the local linear representations of the braid group B 3 and the homogeneous local representations of B n for n ≥ 2. We investigate the connection of these representations with the Burau representation. The linear representations of B n are constructed from the Wada representation of B n in the automorphism group of a free group. 相似文献
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Huiling Li 《Journal of Combinatorial Theory, Series A》2009,116(1):1-11
Suppose that an almost simple group G acts line transitively on a finite linear space S. Let Gx be a point stabilizer in G and suppose that G has socle T, a simple group of Lie type. In this paper we show that if T∩Gx is a parabolic subgroup of T, then G is flag transitive on S. 相似文献