Artin braids and the groups and spaces connected with them

We present a method for computing the number of epimorphisms from a finitely-presented group G to a finite solvable group \Gamma, which generalizes a formula of G\"aschutz. Key to this approach are the degree 1 and 2 cohomology groups of G, with certain twisted coefficients. As an application, we count low-index subgroups of G. We also investigate the finite solvable quotients of the Baumslag-Solitar groups, the Baumslag parafree groups, and the Artin braid groups.Comment: 30 pages; accepted for publication in the Journal of Algebr

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“…In addition to our own results, we use in crucial fashion results of Artin [1], Gorin and Lin [13], and Lin [22][23][24].…”

Section: Finite Quotients Of Braid Groupsmentioning

confidence: 95%

Counting homomorphisms onto finite solvable groups

Matei

Suciu

2005

Journal of Algebra

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“…The fundamental group of the similar space of non-ordered sets is called simply the braid group with N strings, see [8]. For algebraic and homological properties of these groups see, in particular, [51], [4], [40], [66].…”

Section: Basic Example: Cohomology Rings Of Pure Braid Groupsmentioning

confidence: 99%

Topology of plane arrangements and their complements

Vasiliev¹

2001

Russ. Math. Surv.

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This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of graphs, Orlik-Solomon rings, Salvetti complex, matroids, Spanier-Whitehead duality, twisted homology groups, monodromy theory and multidimensional hypergeometric functions.The emphasis on the most geometrical explanation is done; applications and analogies in the differential topology are outlined.Some recent results of the theory are presented.

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“…They fit into the exact sequence Now we describe the Brieskorn corepresentation for BX, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. of a group G. ~o~G = (~;=1 7qG is the nilpotent residue of G. Let X, be a Coxeter group generated by orthogonal reflections in R".…”

Section: Notationmentioning

confidence: 99%

“…The only known corepresentation of generalized pure braid groups is that of the A n group, the classical Burau corepresentation ( [2], [14], [15]). The only known corepresentation of generalized pure braid groups is that of the A n group, the classical Burau corepresentation ( [2], [14], [15]).…”

Section: O Introductionmentioning

confidence: 99%

The D n generalized pure braid group

Markushevich

1991

Geom Dedicata

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Artin braids and the groups and spaces connected with them

Cited by 12 publications

References 98 publications

Counting homomorphisms onto finite solvable groups

Counting homomorphisms onto finite solvable groups

Topology of plane arrangements and their complements

The D n generalized pure braid group

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