| Abstract: |
| In this talk, we will present how to apply a recently developed Floer theory on a fillable contact manifold, called the contact Hamiltonian Floer homology, to generate a homological machinery that replaces the classical Givental non-linear Maslov indices. As a key step, we will emphasize the role of the homological mapping cone from this Floer theory (called a Floer cone) and its fundamental role in reflecting local data of periodic orbits. As an application, the multiplicity of translated points, serving as a natural generalization of fixed points in contact Hamiltonian dynamics, will be deduced. This talk is based on joint work with Dylan Cant, Eric Kilgore, and Igor Uljarevic. |
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