Piecewise visual, linearly connected metrics on boundaries of relatively hyperbolic groups

Suppose a finitely generated group [Formula: see text] is hyperbolic relative to set of proper subgroups text]. Established results in the literature imply that “visual” metric on “linearly connected” if and only boundary has no cut point. Our goal produce linearly connected metrics are “piecewise” visual when contains points. main theorem graph groups decompositions relatively by work B. Bowditch. We describe piecewise boundaries groups. agrees with limit sets vertex this sense visual.