Let $ c_1,c_2,c_3,c_4,c_5$ be a five chain of circles on a genus 2 surface (i.e $ i(c_k,c_{k+1})=1$ and zero otherwise). Then $ (T_{c_1} T_{c_2})^6 = (T_{c_4} T_{c_5})^6 = T_c$ where $ c$ is a separating curve that bounds a neighborhood of $ c_1$ and $ c_2$ (and also bounds a neighborhood of $ c_4$ and $ c_5$ ). This follows from the two chain relation. Then we can think of $ (T_{c_1} T_{c_2})^3$ and $ (T_{c_4} T_{c_5})^3$ as square roots of $ T_c$ . Are these two equal as mapping classes?