Topology and Geometric Group Theory Seminar

Lvzhou ChenUniversity of Texas, Austin
Topology Festival Pre-talk: Stable torsion length

Tuesday, May 11, 2021 - 1:00pm
Via Zoom

Many interesting groups are generated by torsion elements, for instance, mapping class groups, SL(n,Z) and $\mathrm{Homeo}^+(S^1)$. The word length with respect to this typically infinite generating set is called the torsion length. That is, the torsion length tl(g) of an element g is the smallest k such that g is the product of $k$ torsion elements. The stable torsion length stl(g) is the limit of $tl(g^n)/n$, which measures the growth of the torsion length. I will explain how to use topological methods (and planar surfaces) to compute stl(g) in free products of finite abelian groups. The nature of the method implies that stl(g) is always rational in these free products. This is joint work with Chloe Avery.