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decomposition of front diagrams and generating families of functions


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.