On the Hofer Girth of the Sphere of Great Circles

Abstract: An equator of $S^2$ is an embedded circle that divides the sphere into two equal area discs. Chekanov introduced a distance function on the space of equators, induced by the Hofer norm. We define the Hofer girth of this space, roughly speaking, as the smallest diameter of a non-contractible sphere in this space, as inspired by the classic metric invariant of systoles. A somewhat natural embedding of $S^2$ in the space of equators sends each point to the great circle perpendicular to it; this embedding is called the sphere of great circles. In this talk we will discuss a few properties of Hofer girth, and show that the diameter of the sphere of great circles is not optimal, by constructing a strictly better candidate.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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