Mathematical Sciences: Homological Localizations and Homotopy Limits

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8902272 Bousfield Professor Bousfield will continue his research on homological localization of spectra and spaces, together with his research on the general homotopy and homology properties of mapping spaces and other homotopy inverse limit spaces. He is working toward a complete algebraic modeling of K-theoretically localized stable homotopy theory using a united K-homology theory which combines the complex, real, and self-conjugate theories, and he plans increasingly to investigate unstable K-localizations. In other work, Professor Bousfield has established an array of strong convergence theorems for homotopy and homology spectral sequences of cosimplicial spaces, and is developing a general cosimplicial obstruction theory. Building on this, he plans to investigate further unstable Adams spectral sequences for inverse limit spaces, as well as their homology analogues and the associated obstruction theories.