2 citations · 3 across the 5 of their papers we have counts for
6 papers
Knots Connected by Wide Ribbons
Susan C. Brooks, Oguz Durumeric, Jonathan Simon
A ribbon is, intuitively, a smooth mapping of an annulus in 3-space having constant width . This can be formalized as a triple $(x,\varepsilon, \mathbf{…
Unsolvable problems about higher-dimensional knots and related groups
F. Gonzalez-Acuna, C. McA. Gordon, J. Simon
We consider classes of fundamental groups of complements of various kinds of codimension 2 embeddings and show that, in general, the problem of deciding whether or not a group in o…
Mobius transformations of polygons and partitions of 3-space
Richard Randell, Jonathan Simon, Joshua Tokle
The image of a polygonal knot K under a spherical inversion of R^3 (union infinity) is a simple closed curve made of arcs of circles, having the same knot type as the mirror image…
Total Curvature and Packing of Knots
Gregory Buck, Jonathan Simon
We establish a new fundamental relationship between total curvature of knots and crossing number. If K is a smooth knot in 3-space, R the cross-section radius of a uniform tube nei…
Polygonal approximation and energy of smooth knots
Eric J. Rawdon, Jonathan K. Simon
We establish a fundamental connection between smooth and polygonal knot energies, showing that the Minimum Distance Energy for polygons inscribed in a smooth knot converges to the…
Moebius energy of thick knots
Eric J. Rawdon, Jonathan Simon
The Moebius energy of a knot is an energy functional for smooth curves based on an idea of self-repelling. If a knot has a thick tubular neighborhood, we would intuitively expect t…