Journal of Symplectic Geometry

Volume 9 (2011)

Number 2

Equivariant homology for generating functions and orderability of lens spaces

Pages: 123 – 146



Sheila Sandon


In her PhD thesis, Milin developed a $Z_k$-equivariant version of the contact homology groups constructed in Geometry of contact transformations and domains: orderability vs squeezing, "Geom. Topol." 10 (2006), 1635-1747 and used it to prove a $Z_k$-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 Contact homology, capacity and non-squeezing in $R^2n × S^1$ via generating functions, "Ann. Inst. Fourier (Grenoble)" 61 (2011), 145-185. As Milin showed, this result implies orderability of lens spaces.

Published 21 June 2011