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SUMMARY:Inessential Brown-Peterson homology and bordism of elementary abel
 ian groups - Bernhard Hanke\, University of Augsburg
DTSTART:20150429T150000Z
DTEND:20150429T160000Z
UID:TALK58648@talks.cam.ac.uk
CONTACT:Jake Rasmussen
DESCRIPTION:We compute the equivariant bordism of free oriented (Z/\np)^n^
  manifolds\nas a module over \\Omega^SO^\, when p is an \nodd prime.   We 
 show\, among others\,  that this module \nis canonically isomorphic to a d
 irect sum of suspensions of \nmultiple tensor products of \\Omega^SO^(B Z/
 p)\, and that it is\ngenerated by products of standard \nlens spaces. This
  considerably improves previous calculations by various\nauthors. \n\nOur 
 approach relies on the investigation of the  submodule of the\nBrown-Peter
 son homology\nof B(Z /p)^n^ generated by elements coming from proper subgr
 oups\nof (Z/p)^n^.\n\nWe apply our results to the Gromov-Lawson-Rosenberg 
 conjecture for\natoral \nmanifolds whose fundamental groups are elementary
  \nabelian of odd order.\n
LOCATION:MR13
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