论文标题
不可定向的切片表面和铭文矩形
Non-orientable slice surfaces and inscribed rectangles
论文作者
论文摘要
我们讨论具有给定的圆环结或2桥结的4球中平滑和局部不可取向表面的属之间的差异。特别是，我们确定Batson对圆环结的平滑4摄氏度的结果不存在于本地灯泡类别中。我们进一步表明，某些圆环结的家族不是4球和其他4个manifolds中嵌入的Möbius频段的边界。 我们对具有边界的不可定向表面的调查是由给定的圆环结的动机，我们的方法是在约旦曲线中统一存在刻有铭文正方形的证据和具有纵横比$ \ sqrt3 $的刻有矩形的证据。这概括了Hugelmeyer对Jordan曲线平滑的结果。
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 $\sqrt3$ in Jordan curves with a regularity condition. This generalizes a result by Hugelmeyer for smooth Jordan curves.
