Branched Manifolds, knotted Surfaces and Dynamical Systems

: The main goal of this paper is to introduce part of a new approach of proving the existence of a nontrivial knot on any embedded template. This proof in branched 2-manifold case, independent of Bennequin's inequality[Ghrist, 1997], which we make by first showing our simple template contains a nontrivial knot and then showing such a template can be contained in all templates that meet certain conditions as a subtemplate, enables us to generalize it later in this paper to certain forms of 3-template in four dimensional dynamical systems by simply using the device of `spinning' the knot with the corresponding lower dimensional template to obtain the spun knotted surface.

• Type: Journal
• Year: 2008
• Where: IJBC
• Authors: W. Chen, Stephen P. Banks
• Keywords: Embedded Template, IJBC 2006, IJBC 2008, Main Goal, Nontrivial Knot