Comparing geometric intersection numbers. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T12:20:21Z http://mathoverflow.net/feeds/question/22572 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/22572/comparing-geometric-intersection-numbers Comparing geometric intersection numbers. jmortada 2010-04-26T07:57:32Z 2010-04-26T07:57:32Z <p>Let $a$, $b$, and $c$ be simple closed curves in an orientable surface $S$ such that $i(a,b) \geq 2$, $i(a,c) \geq 1$, and $i(b,c) = 0$. Let $w$ be a nontrivial element of the free group $\langle T_a,T_b \rangle$ which is different from $T_a^p$, $p$ nonzero integer, and set $x = w(a)$. If $i(a,x) > i(b,x)$ and $n$ is a nonzero integer, is there a way to compare $i(a,T_c^n(x))$ and $i(b,T_c^n(x)) = i(b,x)$ ?</p>