# Shortening the Hofer length of Hamiltonian circle actions - Mathematics > Symplectic Geometry

Shortening the Hofer length of Hamiltonian circle actions - Mathematics > Symplectic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: A Hamiltonian circle action on a compact symplectic manifold is known to be aclosed geodesic with respect to the Hofer metric on the group of Hamiltoniandiffeomorphisms. If the momentum map attains its minimum or maximum at anisolated fixed point with isotropy weights not all equal to plus or minus one,then this closed geodesic can be deformed into a loop of shorter Hofer length.In this paper we give a lower bound for the possible amount of shortening, andwe give a lower bound for the index -number of independent shorteningdirections-. If the minimum or maximum is attained along a submanifold B, thenwe deform the circle action into a loop of shorter Hofer length whenever theisotropy weights have sufficiently large absolute values and the normal bundleof B is sufficiently un-twisted.

Author: ** Yael Karshon, Jennifer Slimowitz**

Source: https://arxiv.org/