Georgia Institute of Technology College of Sciences

Satellite operations are one of the most basic operations in knot theory. Many researchers have studied the behavior of knot Floer homology under satellite operations. Most of these results use Lipshitz, Ozsvath and Thurston's bordered Heegaard Floer theory. In this talk, we discuss a new technique for studying these operators, and we apply this technique to a family of operators called L-space operators. Using this theory, we are able in many cases to give a simple formula for the behavior of the concordance invariant tau under such operators. This formula generalizes a large number of existing formulas for the behavior of tau under satellite operations (such as cabling, 1-bridge braids and generalized Mazur patterns), and also has a number of topological applications. This is joint work with Daren Chen and Hugo Zhou.