Comparison of Homologies and Automatic Extensions of Invariant Distributions - Chen, Yangyang (Acta mathematica scientia, 2023)
Let G be a reductive Nash group, acting on a Nash manifold X . Let Z be a G -stable closed Nash submanifold of X and denote by U the complement of Z in X . Let χ be a character of G and denote by g the complexified Lie algebra of G . We give a sufficient condition for the natural linear map H k ( g , S ( U ) ⊗ χ ) → H k ( g , S ( X ) ⊗ χ ) between the Lie algebra homologies of Schwartz functions to be an isomorphism. For k = 0, by considering the dual, we obtain the automatic extensions of g -invariant (twisted by - χ ) Schwartz distributions.