Convergence of Baumslag-Solitar groups

Details Convergence of Baumslag-Solitar groups Convergence of Baumslag-Solitar groups

2004-03-15

arxiv.org/abs/math/0403241v3

Mathematics

Group Theory

16 pages, no figure. Notation changes and minor corrections. To appear in Bulletin of the Belgian Mathematical Society -- Simo

Scientific paper

We study convergent sequences of Baumslag-Solitar groups in the space of marked groups. We prove that BS(m,n) --> F_2 for |m|,|n| --> \infty and BS(1,n) --> Z \wr Z for |n| --> \infty. For m fixed, |m|>1, we show that the sequence (BS(m,n))_n is not convergent and characterize many convergent subsequences. Moreover if X_m is the set of BS(m,n)'s for n relatively prime to m and |n|>1, then the map BS(m,n) \mapsto n extends continuously on the closure of X_m to a surjection onto invertible m-adic integers.

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