Convergence of Baumslag-Solitar groups
Abstract
We study convergent sequences of Baumslag-Solitar groups in the space of marked groups. We prove that BS(m,n) --> F2 for |m|,|n| --> ∞ and BS(1,n) --> Z Z for |n| --> ∞. For m fixed, |m|>1, we show that the sequence (BS(m,n))n is not convergent and characterize many convergent subsequences. Moreover if Xm is the set of BS(m,n)'s for n relatively prime to m and |n|>1, then the map BS(m,n) n extends continuously on the closure of Xm to a surjection onto invertible m-adic integers.
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