Generalizations of the Pontryagin and Husain-Kucha actions to manifolds with boundary

In this paper we study a family of generalizations of the Pontryagin and Husain-Kuchar 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-Kuchar 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.