Smooth Equivariant Triangulations of G-Manifolds for G a Finite Group.
Define for a smooth compact hypersurface of its crumpleness as the ratio , where is the distance from to its central set. (In other words, is the maximal radius of an open non-selfintersecting tube around in We prove that any -dimensional non-singular compact algebraic hypersurface of degree is rigidly isotopic to an algebraic hypersurface of degree and of crumpleness . Here , depend only on , and rigid isotopy means an isotopy passing only through hypersurfaces of degree...
We show that there exist non-trivial piecewise linear (PL) knots with isolated singularities , n ≥ 5, whose complements have the homotopy type of a circle. This is in contrast to the case of smooth, PL locally flat, and topological locally flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial.