Geometric versus homotopy theoretic equivariant bordism
Algebraic Topology
2007-05-23 v2 Geometric Topology
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 = 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.
Cite
@article{arxiv.math/0412550,
title = {Geometric versus homotopy theoretic equivariant bordism},
author = {Bernhard Hanke},
journal= {arXiv preprint arXiv:math/0412550},
year = {2007}
}
Comments
19 pages, minor inaccuracies removed, to appear in Math. Ann