2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77566We 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.Corrections to the proof of the main theorem and the statement of Theorem 4.3; AMS-LaTeX, 14 pages. Proceedings of the International Workshop on Topology, M. Farber, W. Lueck, and S. Weinberger (Editors); Publ. AMS, Contemporary Math. Series (to appear)Differential GeometryAlgebraic TopologySymplectic Geometry53C15, 57R85, 57R90, 58F05text