The mapping class group and a theorem of Masur-Wolf (Q1304867)

Masur and Wolf proved in 1995 that the Teichmüller space of genus \(g>1\) surface with the Teichmüller metric is not a Gromov hyperbolic space. This paper provides a new proof of this result based upon a study of the action of the mapping class group on Teichmüller space. For more details, in order for Teichmüller space to be Gromov hyperbolic, the isometries of Teichmüller space must be governed by Gromov's classification of isometries of Gromov hyperbolic space. The main result is obtained by showing that this classification is incompatible with the structure of the mapping class group.