Genus, Fiberedness, τ and ε of Satellite Knots with n-Twisted Generalized Mazur patterns

We study a family of $(1,1)$-pattern knots that generalize the Mazur pattern, and compute the concordance invariants τ and ε of n-twisted satellites formed from these patterns. We show that none of the n-twisted patterns from this family act surjectively on the smooth or rational concordance group. We also determine when the n-twisted generalized Mazur patterns are fibered in the solid torus, compute their genus in S¹ × D², and show that n-twisted satellites with generalized Mazur patterns and non-trivial companions are not Floer thin.