Add to Outlook calendar Add to Google calendar
Title: Roots of Dehn twists
Speaker: Prof. Kashyap Rajeevsarathy IISER Bhopal
Date: 13 December 2011
Time: 11:00 a.m. - 12:00 noon
Venue: Department of Mathematics, Lecture Hall I

Let $F$ be a closed orientable surface of genus $g \\geq 2$ and $C$ be a simple closed curve in $F$. Let $t_C$ denote a left-handed Dehn twist about $C$. When $C$ is a nonseparating curve, D. Margalit and S. Schleimer showed the existence of such roots by finding elegant examples of roots of $t_C$ whose degree is $2g + 1$ on a surface of genus $g + 1$. This motivated an earlier collaborative work with D. McCullough in which we derived conditions for the existence of a root of degree $n$. We also showed that Margalit-Schleimer roots achieve the maximum value of $n$ among all the roots for a given genus. Suppose that $C$ is a separating curve in $F$. First, we derive algebraic conditions for the existence of roots in Mod$(F)$ of the Dehn twist $t_C$ about $C$. Finally, we show that if $n$ is the degree of a root, then $n \\leq 4g^2 + 2g$, and for $g \\geq 10$, $n \\leq \\frac{16}{5}g^2+ 12g + \\frac{45}{4}$.


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 18 Apr 2024