| Abstract: |
This is joint work with Joel Hass and Abby Thompson. Classically, knots and
links are studied using diagrams, which can be projections onto a plane, or
slices of knots and links by a family of parallel planes. In both cases, a
single projection or normal direction of the family of planes is chosen. We
propose instead to study larger families of planes, choosing all normal
directions lying in a fixed plane, or all possible normal directions or
finally all planes and round spheres to slice a given knot or link. These
family of planes have k parameters where k=1,2,3,4 and give rise to natural
invariants. Some connections to the curvature of knots and links will be
outlined, following ideas of Milnor.
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