Luis Celso Chan-Palomo

Facultad de Matemáticas,
Universidad Autónoma de Yucatán, Mérida,
Yuc. 97205, MEXICO.

Title: Reducible and Toroidal Handle Additions

Abstract: Let $M$ be a compact connected orientable hyperbolic 3-manifold and $F$ be a boundary component of $M$ with genus at least two. A slope on $F$ is an isotopy class of essential simple closed curves on $F$. Suppose $M[\alpha]$ and $M[\beta]$ are 3-manifolds obtained by doing 2-handle additions on $M$ along two separating slopes $\alpha$ and $\beta$ on $F$, respectively. The distance between two slopes $\alpha$ and $\beta$ on $F$, denoted by $\Delta(\alpha,\beta)$, is the minimal geometric intersection number among all the curves representing the slopes. In this talk I will estimate $\Delta(\alpha,\beta)$ by combinatorial methods when $M[\alpha]$ is toroidal and $M[\beta]$ is reducible or toroidal.