Ian Zemke
University of Oregon
Title
L-space satellite operators and knot Floer homology
Abstract
Satellite operators are an important subject in knot theory. Many authors have studied the effect of satellite operations on knot Floer homology, though there are still many open questions. Most authors have used the bordered theory of Lipshtiz, Ozsvath and Thurston. There are some very helpful reformulations of these algorithms in terms of immersed curve invariants of Hanselman, Rasmussen and Watson. In this talk we will give a different approach, using the link surgery theorem of Manolescu and Ozsvath. We will consider the family of satellite operators where the corresponding 2-component link is an L-space link. (This family includes all cabling patterns, the Whitehead pattern, as well as a family of generalized Mazur patterns). For such operators, we will describe how to compute the full knot Floer complex of the satellite knot in terms of the knot Floer complex of the original knot as well as the Alexander polynomials of the corresponding pattern link. A key algebraic result is a computation of the link Floer complex of 2-component L-space links in terms of their Alexander polynomials. This is joint work with Daren Chen and Hugo Zhou and the computation of 2-component L-space link complexes is related to earlier joint work with Maciej Borodzik and Beibei Liu.
