Document Type
Lecture
Publication Date
9-17-2015
Abstract
Arnold made an important conjecture in the 70s, relating the number of periodic orbits of a Hamiltonian system to topological information about the manifold. This question has now been (mostly) settled, starting with the work of Floer who used these periodic orbits to construct a homology theory. This work was then extended by Cieliebak, Floer, Hofer and later Viterbo to develop Symplectic Homology. I will provide an overview of this theory and of its applications, and present joint work with Diogo on computing this invariant in a class of examples. In particular, we will see a relationship with (complex) algebraic geometry.
Relational Format
presentation
Recommended Citation
Lisi, Samuel, "Symplectic homology and loop spaces" (2015). Dynamical Systems Seminar. 12.
https://egrove.olemiss.edu/math_dynamical/12
