Geometric versus homotopy theoretic equivariant bordism

Details Geometric versus homotopy theoretic equivariant bordism Geometric versus homotopy theoretic equivariant bordism

2004-12-31

arxiv.org/abs/math/0412550v2

Mathematics

Algebraic Topology

19 pages, minor inaccuracies removed, to appear in Math. Ann

Scientific paper

By 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.

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