Pseudo-Anosov actions on the complex of curves

Vaibhav Gadre (Glasgow)

Monday 7th March, 2016 16:00-17:00 Maths 522


Generalising the classification of elements in SL(2,Z), Thurston gave a classification of elements of mapping class groups as finite order, reducible and pseudo-Anosov. They can be detected from their actions on the complex of curves which is Gromov hyperbolic. For finite order and reducible elements, some power fixes a multi-curve. On the other hand, pseudo-Anosov maps act as loxodromic isometries of the curve complex. In joint work with Tsai, we study bounds in terms of genus on the smallest stable translation lengths. We indicate how these bounds compare to bounds by Penner also later studied by McMullen on the smallest dilatation. Time permitting we will also discuss other aspects of pseudo-Anosov actions on the complex of curves. 

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