Twisted Mazur pattern satellite knots and bordered Floer theory

TL;DR

This paper uses bordered Floer theory to analyze twisted Mazur pattern satellite knots, revealing their Floer homological properties, 3-genus, fibered status, and verifying the Cosmetic Surgery Conjecture for many cases.

Contribution

It provides new insights into the Floer homology, genus, and fiberedness of twisted Mazur pattern satellite knots using bordered Floer theory.

Findings

Q_n(K) is not Floer homologically thin in most cases

Calculated the 3-genus of Q_n(K) based on n and K

Verified the Cosmetic Surgery Conjecture for many satellite knots

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.