Uniform stable commutator length conjecture for arithmetic hyperbolic manifolds

About 20 years old · traced to

Let MM be an arithmetic hyperbolic nn-manifold, let a∈π1(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 a∈π1(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.

References

Primary source

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

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.