Twisted Mazur pattern satellite knots and bordered Floer theory

Abstract

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

40 pages, 11 figures, 16 tables. Improved exposition, corrected some mistakes, modified statement of Theorem 1.0.7. To appear in Michigan Mathematical Journal