Non-orientable Slice Surfaces and Inscribed Rectangles

We discuss differences between genera of smooth and locally-flat non-orientable surfaces in the 4-ball with boundary a given torus knot or 2-bridge knot. In particular, we establish that result by Batson on 4-genus knots does not hold category. further show certain families are an embedded Mobius band other 4-manifolds. Our investigation is motivated our approach to unify proof existence inscribed squares rectangles aspect ratio $\sqrt3$ Jordan curves regularity condition. This generalizes Hugelmeyer for curves.