Mathematics Colloquia and Seminars
Return to Colloquia & Seminar listing
decomposition of front diagrams and generating families of functionsGeometry/Topology
|Speaker: ||BATS at Davis: Dmitry Fuchs, UCDavis|
|Location: ||1147 MSB|
|Start time: ||Tue, Apr 24 2007, 2:30PM|
A front diagram (of a Legendrian knot in the standard contact space) is a
closed curve in the plane (x,z) with cusps and without vertical tangents and self-tangencies.
A generic family f_t of functions of n real variables x_1,...,x_n such that
F_t(x)=x_n for large |t| and large |x| is called a generating family of functions for a front
diagram L if L is the set of pairs (t,c) such that c is a critical value of f_t. When does a
front diagram possess a generating family of functions? A necessary and sufficient
condition for that is simultaneously a necessary and sufficient condition for several other,
seemingly unrelated, properties of the front diagram.