Luis Gerardo Valdez-Sánchez

Department of Mathematical Sciences,
The University of Texas at El Paso,
El Paso, Texas 79968, USA.

Title: Reducible Dehn fillings of 3-manifolds

Abstract: The Cabling of Conjecture of Gonzalez-Acuña and Short states that the only knots in the 3-sphere which admit a reducible Dehn surgery are the cable knots. In this talk we summarize some known results about reducible Dehn fillings of 3-manifolds and their impact on the cabling conjecture. We will also discuss the use of properties of graphs of intersection of surfaces in the analysis of reducible Dehn fillings as developed by Gordon-Luecke and others.

Title: Toroidal Dehn fillings of 3-manifolds

Abstract: In this talk we will discuss the transition from reducible to toroidal Dehn fillings from the point of view of the technique involving graphs of intersection of surfaces, and present some results and open problems on toroidal Dehn fillings.