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Full-Text Articles in Physical Sciences and Mathematics
Racks, Quandles And Virtual Knots, Victor Samuel Nelson
Racks, Quandles And Virtual Knots, Victor Samuel Nelson
LSU Doctoral Dissertations
We begin with a brief survey of the theory of virtual knots, which was announced in 1996 by Kauffman. This leads naturally to the subject of quandles and quandle homology, which we also briefly introduce. Chapter 2 contains a proof in terms of Gauss diagrams that the forbidden moves unknot virtual knots. This chapter includes material which has appeared in the Journal of Knot Theory and its Ramifications and is reprinted here by permission of World Scientific Publishing. In chapter 3 (cowritten with my advisor R.A.Litherland) we confirm a conjecture of J.S.Carter et.al. that the long exact sequence in rack …
Interlocked Open Linkages With Few Joints, Erik D. Demaine, Stefan Langerman, Joseph O'Rourke, Jack Snoeyink
Interlocked Open Linkages With Few Joints, Erik D. Demaine, Stefan Langerman, Joseph O'Rourke, Jack Snoeyink
Computer Science: Faculty Publications
We advance the study of collections of open linkages in 3-space that may be interlocked in the sense that the linkages cannot be separated without one bar crossing through another. We consider chains of bars connected with rigid joints, revolute joints, or universal joints and explore the smallest number of chains and bars needed to achieve interlock. Whereas previous work used topological invariants that applied to single or to closed chains, this work relies on geometric invariants and concentrates on open chains.