Invariant boundary distributions for finite graphs

Abstract

Let $\Gamma$ be the fundamental group of a finite connected graph $\mathcal{G}$. Let $\mathfrak{M}$ be an abelian group. A {\it distribution} on the boundary $\partial \Delta$ of the universal covering tree $\Delta$ is an $\mathfrak{M}$-valued measure defined on clopen sets. If $\mathfrak{M}$ has no $\chi (\mathcal{G})$-torsion then the group of $\Gamma$-invariant distributions on $\partial \Delta$ is isomorphic to $H_1(\mathcal{G},\mathfrak{M})$.

References in corpus (1)

• Boundary operator algebras for free uniform tree lattices