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The 1996 Joint Spring Topology Conference and Southeast Dynamical Systems Conference
March 7-9, 1996
Ball State University
Muncie, IN, USA

Organizers
John Emert, Kerry Jones, Roger Nelson

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Local Properties of Solutions of a Differential Equation via Normed Linear Spaces
by
Michael A. Karls
Ball State University
Coauthors: Morris W. Hirsch

Motivated by the problem of robot navigation, the following question arises: To what extent can the singularities of a Morse function be prescribed? In particular, can the Morse function vary continuously as a function of the singularities?

I will give some examples of when it can and when it can't. The main theorem is that a family of Morse functions with 3 singularities on the 2-disk can't vary continuously as a function of the singularities. Such a family would induce a homomorphism from the braid group on 3 strands to the braid group on 2 strands. Enough of this homomorphism can be computed to prove that it doesn't exist.

This work is joint with Morris W. Hirsch of U.C. Berkeley.

Date received: January 31, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-38.