Twisted Mazur Pattern Satellite Knots & Bordered Floer Theory

Abstract

We use bordered Floer theory to study properties of twisted Mazur pattern satellite knots ${\mathit{Q}}_{\mathit{n}}(\mathit{K})$. We prove that ${\mathit{Q}}_{\mathit{n}}(\mathit{K})$ is not Floer homologically thin, with two exceptions. We calculate the 3-genus of ${\mathit{Q}}_{\mathit{n}}(\mathit{K})$ in terms of the twisting parameter n and the 3-genus of the companion K, and we determine when ${\mathit{Q}}_{\mathit{n}}(\mathit{K})$ is fibered. As an application to our results on Floer thickness and 3-genus, we verify the Cosmetic Surgery Conjecture for many of these satellite knots.