Uniform stable commutator length conjecture for arithmetic hyperbolic manifolds

Let MM be an arithmetic hyperbolic nn-manifold, let aπ1(M){id}a\in\pi_1(M)\setminus\{\operatorname{id}\} be non-parabolic, and let scl(a)\operatorname{scl}(a) denote the stable commutator length of aa.

Uniform stable commutator length conjecture. For each nn there is a constant C(n)>0C(n)>0 such that, for every arithmetic hyperbolic nn-manifold MM and every non-parabolic aπ1(M){id}a\in\pi_1(M)\setminus\{\operatorname{id}\},

scl(a)C(n).\operatorname{scl}(a)\ge C(n).

This strengthens the preceding uniform lower-bound conjecture by formulating it in terms of stable commutator length. The source gives no evidence of a resolution.

Sources & referencesView supporting material

Primary source

Danny Calegari, “Length and stable length”, arXiv:math/0605354 (2007).

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