The general case of cutting of GML surfaces and bodies

Abstract

Generalized M\"obius-Listing bodies and surfaces are generalizations of the classic M\"obius band. The original motivation is that for solutions of boundary value problems the knowledge of the domain is essential. In previous papers cutting of GML bodies with cross section symmetrical disks with symmetry 2, 3, 4, 5 and 6 have been classified. In this paper we solve the general case, using regular m-gons as cross section. The 3D problem is reduced to the problem of cutting regular m-polygons with d-knives, related to the number of divisors of m. The problem has both a geometrical and topological solution, and has many connections to other fields of mathematics.