Moscow Arnold's seminar
4.11.2000

Some invariants of admissible homotopies of space curves
V.D. Sedykh

A regular homotopy of a generic curve in projective 3-space is called
admissible if it defines a generic one-parameter family of curves where
every curve has no self-intersections and inflection points, is not
tangent to a smooth part of its evolvent, and has no tangent planes
osculating to the curve at two different points.
We indicate some invariants of admissible homotopies of space curves
and prove, in particular, that the number of flattening points of the
curve x=cos t, y=sin t, z=cos 3t can not vanish in a process of
admissible homotopies.