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We study the Hamiltonian formulation of the generally covariant theorydefined by the Lagrangian 4-form L=e_I e_J F^{IJ}(\omega) where e^I is a tetradfield and F^{IJ} is the curvature of a Lorentz connection \omega^{IJ}. Thistheory can be thought of as the limit of the Holst action for gravity for theNewton constant G goes to infinity and Immirzi parameter goes to zero, whilekeeping their product fixed. This theory has for a long time been conjecturedto be topological. We prove this statement both in the covariant phase spaceformulation as well as in the standard Dirac formulation. In the time gauge,the unconstrained phase space of theory admits an SU(2) connection formulationwhich makes it isomorphic to the unconstrained phase space of gravity in termsof Ashtekar-Barbero variables. Among possible physical applications, we arguethat the quantization of this topological theory might shed new light on thenature of the degrees of freedom that are responsible for black entropy in loopquantum gravity.

A topological limit of gravity admitting an SU(2) connection formulation