Generalizations of the Pontryagin and Husain-Kucha\v{r} actions to manifolds with boundary

Understand

In this paper we study a family of generalizations of the Pontryagin and Husain-Kucha\v{r} actions on manifolds with boundary.

• In some cases, they describe well-known models---either at the boundary or in the bulk---such as 3-dimensional Euclidean general relativity with a cosmological constant or the Husain-Kucha\v{r} model.
• We will use Hamiltonian methods in order to disentangle the physical and dynamical content of the systems that we discuss here.
• This will be done by relying on a geometric implementation of the Dirac algorithm in the presence of boundaries recently proposed by the authors.