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In this paper we study a family of generalizations of the Pontryagin andHusain-Kucha\v{r} actions on manifolds with boundary. In some cases, theydescribe well-known models---either at the boundary or in the bulk---such as3-dimensional Euclidean general relativity with a cosmological constant or theHusain-Kucha\v{r} model. We will use Hamiltonian methods in order todisentangle the physical and dynamical content of the systems that we discusshere. This will be done by relying on a geometric implementation of the Diracalgorithm in the presence of boundaries recently proposed by the authors.

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