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.
Functoriality for symplectic and contact cutting, and equivariant radial-squared blowups
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abstract
We exhibit Lerman's cutting procedure as a functor from the category of manifolds-with-boundary equipped with free circle actions near the boundary, with so-called equivariant transverse maps, to the category of manifolds and smooth maps. We then apply the cutting procedure to differential forms that are not necessarily symplectic, to distributions that are not necessarily contact, and to submanifolds. We obtain an inverse functor from so-called equivariant radial-squared blowup.
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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.