Genus, Fiberedness, and 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 and 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.