Twisted Mazur Pattern Satellite Knots & Bordered Floer Theory

Abstract

We use bordered Floer theory to study properties of twisted Mazur pattern satellite knots Qn(K). We prove that Qn(K) is not Floer homologically thin, with two exceptions. We calculate the 3-genus of Qn(K) in terms of the twisting parameter n and the 3-genus of the companion K, and we determine when Qn(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.