  This sketch shows that the usual generating function based capacities have an
interpretation in the language of persistent homology as persistences of
certain homology classes in the persistence module formed by the corresponding
generating function homology groups. This viewpoint suggests various new
invariants, in particular a $\mathbb{Z}_k$-equivariant capacity which can be
used to prove orderability of lens spaces, proved by Milin (2008) using contact
homology and by Sandon (2010) using equivariant generating function homology.
These are informal notes originally circulated in January 2014.
