  This paper establishes the existence of a gap for the stable length spectrum
on a hyperbolic manifold. If M is a hyperbolic n-manifold, for every positive e
there is a positive d depending only on n and on e such that an element of
pi_1(M) with stable commutator length less than d is represented by a geodesic
with length less than e. Moreover, for any such M, the first accumulation point
for stable commutator length on conjugacy classes is at least 1/12.
  Conversely, "most" short geodesics in hyperbolic 3-manifolds have arbitrarily
small stable commutator length. Thus stable commutator length is typically good
at detecting the thick-thin decomposition of M, and 1/12 can be thought of as a
kind of homological Margulis constant.
