Hierarchy paths in the Hatcher-Thurston complex (Q1934436)

The author builds on work of \textit{H. A. Masur} and \textit{Y. N. Minsky} [Geom. Funct. Anal. 10, No. 4, 902--974 (2000; Zbl 0972.32011)] and the reviewer [J. Ramanujan Math. Soc. 24, No. 4, 341--357 (2009; Zbl 1195.57042)] and shows that the Hatcher-Thurston complex of a surface \(F\) is an interpolating complex between the pants complex and the curve complex. The grading of the surfaces in the paper under review is genus (unlike the reviewer's work, where the gradation is by complexity). The main Theorem 2.10 of the present paper extends the estimates of Masur-Minsky to the Hatcher-Thurston complex.