An Ascending Hnn Extension of a Free Group Inside
نویسنده
چکیده
We give an example of a subgroup of SL2 C which is a strictly ascending HNN extension of a non-abelian finitely generated free group F . In particular, we exhibit a free group F in SL2 C of rank 6 which is conjugate to a proper subgroup of itself. This answers positively a question of Drutu and Sapir (2005). The main ingredient in our construction is a specific finite volume (non-compact) hyperbolic 3-manifold M which is a surface bundle over the circle. In particular, most of F comes from the fundamental group of a surface fiber. A key feature of M is that there is an element of π1(M) in SL2 C with an eigenvalue which is the square root of a rational integer. We also use the Bass-Serre tree of a field with a discrete valuation to show that the group F we construct is actually free.
منابع مشابه
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