2020/03/03 by Peter Feller, Marco Golla, Feller, Peter +1
Computer Science · Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2003.01590
openalex publication_date 2020/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 a result by Batson on the smooth non-orientable 4-genus of torus knots does not hold in the locally-flat category. We further show that certain families of torus knots are not the boundary of an embedded Möbius band in the 4-ball and other 4-manifolds. Our investigation of non-orientable surfaces with boundary a given torus knot is motivated by our approach to unify the proof of the existence of inscribed squares and of inscribed rectangles with aspect ratio √3 in Jordan curves with a regularity condition. This generalizes a result by Hugelmeyer for smooth Jordan curves.