Mathematical Sciences: Research in Index Foliation Theory

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9504084 Kamber The proposed research is in index and foliation theory with applications to mathematical physics. The proposed problems are central problems in the abstract index theory and have significant applications to gauge theories and anomalies. Foliation reduction techniques introduced earlier by the investigator may prove to have interesting connections to the newly discovered Seiberg-Witten monopole equations. Foliation theory seeks to understand the global behavior of spaces of solutions to ordinary differential equations; index theory assigns integers and other easily identifiable quantities to these spaces and aims to distinguish different spaces by means of their indices. The techniques and results developed here continue to find applications in various parts of mathematical physics.