This is no longer true for R-trees, as Morgan & Shalen (1991) showed that the fundamental groups of surfaces of Euler characteristic less than −1 also act freely on a R-trees.
這結果對R-樹不成立：Morgan & Shalen (1991) 證明了歐拉示性數小於-1的曲面的基本群也自由作用在R-樹上。