Equivariant Homology of Generating Functions and Orderability of Lens Spaces

TL;DR

This paper re-derives an equivariant contact non-squeezing theorem using generating functions, demonstrating that lens spaces are orderable, thus connecting homological invariants with geometric properties.

Contribution

It provides a new proof of an equivariant contact non-squeezing theorem via generating functions, linking homology groups to orderability of lens spaces.

Findings

Re-establishment of the equivariant contact non-squeezing theorem

Demonstration that lens spaces are orderable

Connection between homology groups and geometric orderability

Abstract

In her PhD thesis Milin developed an equivariant version of the contact homology groups constructed by Eliashberg, Kim and Polterovich and used it to prove an equivariant contact non-squeezing theorem. In this article we re-obtain the same result in the setting of generating functions, starting from the homology groups studied in arXiv:0901.3112. As Milin showed, this result implies orderability of lens spaces.