2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73726By results of Loeffler and Comezana, the Pontrjagin-Thom map from geometric G-equivariant bordism to homotopy theoretic equivariant bordism is injective for compact abelian G. If G = S^1 x ... x S^1, we prove that the associated fixed point square is a pull back square, thus confirming a recent conjecture of D. Sinha. This is used in order to determine the image of the Pontrjagin-Thom map for toral G.19 pages, minor inaccuracies removed, to appear in Math. AnnAlgebraic TopologyGeometric Topology55N21, 55N91, 57S15 (primary) 57N75 (secondary)text