TY - JOUR

T1 - Shortening the hofer length of hamiltonian circle actions

AU - Karshon, Yael

AU - Slimowitz, Jennifer

PY - 2015

Y1 - 2015

N2 - A Hamiltonian circle action on a compact symplectic manifold is known to be a closed geodesic with respect to the Hofer metric on the group of Hamiltonian di fieomorphisms. If the momentum map attains its minimum or maximum at an isolated 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, and we give a lower bound for the index (“number of independent shortening directions”). If the minimum or maximum is attained along a submanifold B, then we deform the circle action into a loop of shorter Hofer length whenever the isotropy weights have suficiently large absolute values and the normal bundle of B is s0075ficiently un-twisted.

AB - A Hamiltonian circle action on a compact symplectic manifold is known to be a closed geodesic with respect to the Hofer metric on the group of Hamiltonian di fieomorphisms. If the momentum map attains its minimum or maximum at an isolated 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, and we give a lower bound for the index (“number of independent shortening directions”). If the minimum or maximum is attained along a submanifold B, then we deform the circle action into a loop of shorter Hofer length whenever the isotropy weights have suficiently large absolute values and the normal bundle of B is s0075ficiently un-twisted.

UR - http://www.scopus.com/inward/record.url?scp=84927125497&partnerID=8YFLogxK

U2 - 10.4310/JSG.2015.v13.n1.a6

DO - 10.4310/JSG.2015.v13.n1.a6

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AN - SCOPUS:84927125497

SN - 1527-5256

VL - 13

SP - 209

EP - 259

JO - Journal of Symplectic Geometry

JF - Journal of Symplectic Geometry

IS - 1

ER -