Examples of Simple, Singular, Legendrian, and Legendrian Singular Knots (IMAGE)
Caption
While the knots we are familiar with have loose ends, mathematical knots are formed with closed loops, like rubber bands. A) Simple knots: the first and last knots can be derived from each other without breaking the string, so they are mathematically equivalent. B) Singular knots: opposite crossovers (one formed by the right string passing on top of the left string and the other inverse) are called singular points (star). C) Legendrian knots: purely mathematical objects with their tangent vectors contained in the contact planes (shown in red, pink and blue) are defined by symplectic (contact) geometry. D) Legendrian singular knots (LSK): the focus of this IBS study have both contact planes and singular points.
Credit
IBS
Usage Restrictions
None
License
Licensed content