We define a ribbon knot as a knot that can be embedded into three-dimensional space such that it bounds a ribbon disk, that is, a surface that can be deformed in any topologically valid way, as well as passing any one section of the disc through another completely, with the line of intersection that forming a slit that does not touch the edges of the disc. Let K be a knot, not necessarily a ribbon knot, with crossing number k. We define an algorithm to create a ribbon knot from K which has crossing number at most 4k such that, which we call "ribbon doubling." We also investigate the number of potential ribbon doubles for a knot, and potential restrictions on its crossing number. We propose a partial inverse operation for ribbon doubles, and show that it is not unique. Lastly, we propose a potential lower bound for the crossing number of the ribbon double of a knot. We then relate the concept of a ribbon double to that of a partial knot for symmetric union presentations, and propose a potential technique for selecting a unique ribbon double.
University / Institution: University of Utah
Format: In Person
SESSION C (1:45-3:15PM)
Area of Research: Science & Technology
Faculty Mentor: Edmund Karasiewicz
Location: Union Building, PARLOR A (2:45pm)