Morse-Bott Floer Homology and Rectangular Pegs

The rectangular peg problem, an extension of the square peg problem, is easy to outline but challenging to prove through elementary methods. In this talk, I discuss how to show the existence and a generic multiplicity result assuming the Jordan curve is smooth, utilizing Morse-Bott Floer homology. In particular, we obtain a convenient formula for computing the algebraic intersection number of cleanly intersecting Lagrangian submanifolds, which is well consistent with the Euler characteristic of Morse-Bott Floer homology in the spirit of "categorification''.

Date

Speakers

Zhen Gao

Affiliation

Universität Augsburg