Geometric versus homotopy theoretic equivariant bordism

2004/12/31 by Bernhard Hanke, Hanke, Bernhard
Mathematics · #55N21 #55N91 #57S15 (primary) 57N75 (secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT #msc:55N21 #msc:55N91 #msc:57N75 #msc:57S15

paper · pdf · doi:10.48550/arxiv.math/0412550

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

arxiv created 2005/04/12 · arxiv updated 2009/12/01

Abstract

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 = S¹ x ... x S¹, 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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