The stable commutator length (scl) is a relative version of the Gromov-Thurston norm. It is a group invariant sensitive to geometric and dynamical properties. Many groups that act on non-positively curved spaces are known to have a spectral gap in scl, which is a homological analog of margulis constants for negatively curved manifolds. We will discuss sharp estimates of spectral gaps for groups acting on trees using a topological method. This yields a gap for any 3-manifold group and a new proof for the optimal gap 1/2 by Heuer on all right-angled Artin groups. This is joint work with Nicolaus Heuer.

  

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