2009/04/06 by Blake Winter, Winter, Blake · 1 citation
Mathematics · Computer Science · #Geometric and Algebraic Topology #semigroups and automata theory #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0904.0684
We consider ribbon n-knots for n≥ 2. For such knots we define a set of moves on ribbon disks, and show that any two ribbon disks for isotopic knots are related by a finite sequence of such moves and ambient isotopies. Using this we are able to prove that there is a natural geometric correspondence between ribbon n-knots and ribbon m-knots which is bijective. We also explore a diagrammatic calculus for such knots. In addition we show that for such knots, any two band presentations for the same knot are stably equivalent.