The relation between compact and non-compact equivariant cobordisms
  We show that the theory of stable complex $G$-cobordisms, for a torus $G$, is embedded into the theory of stable complex $G$-cobordisms of not necessarily compact manifolds equipped with proper abstract moment maps. Thus the introduction of such non-compact cobordisms in the stable complex $G$-cobordism theory does not lead to new relations. 
Viktor L. Ginzburg, Victor L. Guillemin, and Yael Karshon