Mathematical Sciences: Brown-Peterson Homology and Duality

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The main thrust of this project is an attempt to find new relationships between homology and homotopy. The long-range goal is to find a connection between spectra on the homology side of the Brown-Peterson spectra and spectra on the sphere side. Some form of symmetry should explain left-right phenomena observed in the generalized homology of its own omega spectrum. A first step in this project is to compute the homology of the spaces in the omega spectra for Ravenel's spectra. Other projects include improving results for non-immersion of products of real projective spaces and a continuing attack on the Johnson question.