Date: Thursday, November 08, 2012
Location: 3866 East Hall (3:00 PM to 4:00 PM)
Title: Links and critical points
Abstract: An extremely useful principle in the calculus of variations--originally due to Rabinowitz et al. and widely used to find solutions to elliptic boundary value problems and periodic orbits of Hamiltonian systems--asserts that if a suitably well-behaved functional separates the two components of a nontrivial link, then a minimax procedure
gives rise to a critical point of the functional, with control over the corresponding critical value. I will present a refinement of this in the model case of Morse functions on compact manifolds, showing that such a function has more critical points than required by the Morse inequalities if and only if it separates a link with nonzero linking number; indeed, there is a precise characterization of the exact number of critical points in terms of the behavior of the function with respect to links. The proof is based on an analysis of the Morse-Smale-Witten complex, using ideas borrowed from chain-level symplectic Floer theory.
Speaker: Michael Usher
Institution: University of Georgia
Event Organizer:
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