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

9731213 Wilson本奖学金资助约翰霍普金斯大学数学系W. Stephen Wilson博士与日本京都大学理科研究生院数学系西田五郎教授进行为期六个月的研究访问。合作者将试图证明一个关于空间不稳定Brown-Peterson同调的猜想。这个猜想是近20年前在美国由美国和日本数学家首次提出的。在美国和日本数学家最近的合作中，在这个问题上取得了重大进展，PI和他的合作者已经勾勒出一种有望解决这个问题的方法。该猜想表明空间的Brown-Peterson同调中的n维元素是第n类无扭转的。合作者将把这个问题转化为一个上同调版本的分类空间，然后证明各种同伦分解定理，这个问题的解决将对美国和日本数学家都有好处。本项目由美国国家科学基金会和日本财团全球伙伴关系中心科学奖学金计划资助。＊＊＊

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. ***