منابع مشابه
The Sigma Invariants of Thompson's Group F
Thompson’s group F is the group of all increasing dyadic PL homeomorphisms of the closed unit interval. We compute Σm(F ) and Σm(F ;Z), the homotopical and homological Bieri-Neumann-Strebel-Renz invariants of F , and show that Σm(F ) = Σm(F ;Z). As an application, we show that, for every m, F has subgroups of type Fm−1 which are not of type FPm (thus certainly not of type Fm).
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We compute the Bieri-Neumann-Strebel-Renz geometric invariants, Σn, of the lamplighter groups Lm by using the Diestel-Leader graph DL(m,m) to represent the Cayley graph of Lm.
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The Product Conjecture for the homological Bieri-Neumann-StrebelRenz invariants is proved over a field. Under certain hypotheses the Product Conjecture is shown to also hold over Z, even though D. Schütz has recently shown that the Conjecture is false in general over Z. Our version over Z is applied in a joint paper with D. Kochloukova [5] to show that for all n Thompson’s group F contains subg...
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There is an equation relating numbers of curves on F0 = P × P satisfying incidence conditions and numbers of curves on F2 satisfying incidence conditions. The purpose of this paper is to give a tropical proof of this equation (for some cases). We use two tropical methods. The first method proves the formula for rational curves. We use induction on the degree and two Kontsevich-type formulas for...
متن کاملInvariants of Group Rings
Since the foundation paper of M. Auslander and 0. Goldman [ 1 J, several authors have generalized constructions for studying group algebras over fields to separable algebras over commutative rings. Specifically, we have in mind the Schur index [20], the Schur exponent [18], the Schur group [S], and the uniform group [ 111. This paper gives additional properties of these constructions and studie...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2010
ISSN: 1661-7207
DOI: 10.4171/ggd/83