Locally standard torus actions are classified up to equivariant diffeomorphism by the triple of their quotient, its unimodular labelling, and a degree-two Chern class.
Davis, Smooth G-manifolds as collections of fibre bundles , Pacific J
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Classification of locally standard torus actions
Locally standard torus actions are classified up to equivariant diffeomorphism by the triple of their quotient, its unimodular labelling, and a degree-two Chern class.