### Fractional powers of Dehn twists about nonseparating curves

- Series
- Geometry Topology Seminar
- Time
- Monday, May 14, 2012 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Kashyap Rajeevsarathy – IISER Bhopal

Let S_g be a closed orientable surface of genus g > 1 and C a simple closed nonseparating curve in S_g. Let t_C denote a left handed Dehn twist about C. A fractional power of t_C of exponent L/n is a h in Mod(S_g) such that h^n = t_C^L. Unlike a root of a t_C, a fractional power h can exchange the sides of C. We will derive necessary and sufficient conditions for the existence of both side-exchanging and side-preserving fractional powers. We will give some applications of the main result in both cases. Finally, we give a complete classification of a certain class of side-preserving and side-exchanging fractional powers on S_5.