Por Stephan Klaus (M. F. I. Oberwolfach).

Abstract: For a differentiable function f:R^n -> R and a regular value y, the level set f^{-1}(y) is a smooth (n-1)-dimensional hypersurface without boundary. Thus it is not possible to construct the Moebius strip in this way as it has a 1-dimensional boundary. However, it is possible to construct a solid Moebius strip, i.e. the 2-dimensional boundary of thickened (but thin) 3-dimensional Moebius strip. In fact, some time ago we constructed 1-, 2- and 3-twisted solid Moebius strips with polynomials f(x,y,z) of order 6, 8 and 10 respectively. In the talk we will present a a simplified construction of a polynomial of degree 4+2r for a solid r-twisted Moebius strip. The construction can be generalized to more complex surfaces with twisted topology such as solid torus knots.