Bavard duality for the relative Gromov seminorm

  • Alexis Marchand

    University of Cambridge, Cambridge, UK
Bavard duality for the relative Gromov seminorm cover

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Abstract

The relative Gromov seminorm is a finer invariant than stable commutator length where a relative homology class is fixed. We show a duality result between bounded cohomology and the relative Gromov seminorm, analogously to Bavard duality for scl. We give an application to computations of scl in graphs of groups. We also explain how our duality result can be given a purely algebraic interpretation via a relative version of the Hopf formula. Moreover, we show that this leads to a natural generalisation of a result of Calegari on a connection between scl and the rotation quasimorphism.

Cite this article

Alexis Marchand, Bavard duality for the relative Gromov seminorm. Enseign. Math. (2024), published online first

DOI 10.4171/LEM/1087