Some non-amenable groups
Aditi Kar, Graham A. Niblo
TL;DR
This paper extends previous work to demonstrate that certain finitely generated groups have a non-zero first l2-Betti number, revealing new insights into their algebraic and geometric properties.
Contribution
It generalizes R. Thomas's result to a broader class of finitely generated groups, establishing the non-vanishing of their first l2-Betti number.
Findings
Non-vanishing of the first l2-Betti number for specific groups
Extension of Thomas's result to new group classes
Implications for group theory and topology
Abstract
We generalize a result of R. Thomas to establish the non-vanishing of the first l2-Betti number for a class of finitely generated groups.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Finite Group Theory Research · Geometric and Algebraic Topology