Inessential Brown-Peterson homology and bordism of elementary abelian groups

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• Bernhard Hanke, University of Augsburg
• Wednesday 29 April 2015, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Jake Rasmussen.

We compute the equivariant bordism of free oriented (Z/ p)ⁿ manifolds as a module over \Omega^SO, when p is an odd prime. We show, among others, that this module is canonically isomorphic to a direct sum of suspensions of multiple tensor products of \Omega^SO(B Z/p), and that it is generated by products of standard lens spaces. This considerably improves previous calculations by various authors.

Our approach relies on the investigation of the submodule of the Brown-Peterson homology of B(Z /p)ⁿ generated by elements coming from proper subgroups of (Z/p)ⁿ.

We apply our results to the Gromov-Lawson-Rosenberg conjecture for atoral manifolds whose fundamental groups are elementary abelian of odd order.

This talk is part of the Differential Geometry and Topology Seminar series.

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