Notes on tangles, 2-handle additions and exceptional Dehn fillings

This paper is a set of notes concerning the following related topics in 3-manifold topology: n-strand tangles, handle addi-tions, the cabling conjecture, and exceptional Dehn fillings. 1. Introduction. In this paper we consider several related problems in 3-manifold topology. Here is a brief description of the content and organization of the paper. Definitions of terms which occur can be found in relevant sections. Classical tangles, i.e., tangles in a 3-ball, have been heavily studied. Her