The BV pushforward of standard Palatini-Cartan gravity on Sigma x I equals the restricted BV theory, which is isomorphic to the AKSZ theory compatible with BFV boundary data.
On the properties of coframes
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abstract
We consider injectivity and surjectivity of some maps on the exterior algebra of isomorphic finite-dimensional vector spaces. We prove the properties of the maps in full generality, for any dimension of the vector space and any subspace. We also draw a connection with the Palatini-Cartan formulation of General Relativity, for which these maps are of crucial importance.
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BV Pushforward of Palatini-Cartan gravity
The BV pushforward of standard Palatini-Cartan gravity on Sigma x I equals the restricted BV theory, which is isomorphic to the AKSZ theory compatible with BFV boundary data.