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Geometric Invariants for Artin Groups
Author(s) -
Meier J
Publication year - 1997
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611597000063
Subject(s) - mathematics , invariant (physics) , abelian group , pure mathematics , iterated function , solvable group , combinatorics , torus , mathematics subject classification , mathematical analysis , geometry , mathematical physics
The Bieri‐Neumann‐Strebel invariant of a finitely generated group G determines, among other things, whether or not a given normal subgroup N , with G / N abelian, is finitely generated. We examine the BNS‐invariants of “Pride groups”, a large class of groups containing the Artin groups; in particular we establish a criterion which implies that a character χ of a Pride group G G is in the BNS‐invariant Σ 1 ( G G). This restricts in the case of an Artin group A G to a simple condition which implies a character is in Σ 1 ( A G). As an application this can be used to compute the unit ball in the Thurston semi‐norm for the complement of iterated connected sums of (2, n )‐torus links. 1991 Mathematics Subject Classification : 20F36, 20E07.