NSF-CGP Fellowship: A Japan -U.S. Attack on the Unstable Brown-Peterson Homology of Spaces

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9731213 Wilson This award provides funds to support a six month research visit by Dr. W. Stephen Wilson, Department of Mathematics, Johns Hopkins University, for collaboration with Professor Goro Nishida, Division of Mathematics, Graduate School of Science, Kyoto University, Japan. The collaborators will attempt to prove a conjecture on the unstable Brown-Peterson homology of spaces. This conjecture was first made nearly 20 years ago in the USA by American and Japanese mathematicians. In recent collaboration between U.S. and Japanese mathematicians, significant progress has been made on the problem, and the PI and his collaborators have sketched an approach which is expected to resolve the question. The conjecture states that n-dimensional elements in the Brown-Peterson homology of a space are an n-th type of torsion free. The collaborators will translate the problem into classifying spaces for a cohomology version and then prove various homotopy decomposition theorems Solution of the problem will be of mutual benefit to U.S. and Japanese mathematicians. This project is supported under the Science Fellowship Program between the National Science Foundation and the Japan Foundation Center for Global Partnership. ***