Inspired by works of Masur-Minsky and Mahan Mj, we observe that the Hatcher-Thurston complex of a surface F is an interpolating complex between the pants complex and the curve complex, then we give a hierarchical stru...Inspired by works of Masur-Minsky and Mahan Mj, we observe that the Hatcher-Thurston complex of a surface F is an interpolating complex between the pants complex and the curve complex, then we give a hierarchical structure for the Hatcher-Thurston complex. By this hierarchical structure, we show a distance formula in the Hatcher-Thurston complex related to subsurfaces of positive genera. As a corollary, we show that the Hatcher-Thurston complex has one end for surface with genus at least three, the proof runs the same line as a result of Masur-Schleimer, the key tool is the distance formula.展开更多
基金supported in part by RFDP 200802461001National Natural Science Foundation of China (Grant No. 10901038)
文摘Inspired by works of Masur-Minsky and Mahan Mj, we observe that the Hatcher-Thurston complex of a surface F is an interpolating complex between the pants complex and the curve complex, then we give a hierarchical structure for the Hatcher-Thurston complex. By this hierarchical structure, we show a distance formula in the Hatcher-Thurston complex related to subsurfaces of positive genera. As a corollary, we show that the Hatcher-Thurston complex has one end for surface with genus at least three, the proof runs the same line as a result of Masur-Schleimer, the key tool is the distance formula.
