Mathematical Sciences: Geometry and Analysis of Foliations

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9400676 Heitsch Professor Heitsch will continue research on Bismut superconnections and the Chern character for operators defined along leaves of a foliation. Further collaboration with C.Lazarov will be done on the extension of analytic invariants for compact manifolds to invariants of foliations and of open manifolds, with special emphasis on torsion invariants. A development will be made of coarse cohomology and coarse invariants for maps of topological spaces. The geometry of foliations will also be investigated through the indices of transversally ellipticoperators. Geometric objects are often classified by determining whether they can be mapped or deformed into standard geometric objects. Certain geometric invariants, for example, the number of "holes" are preserved under such maps. This project involves invariants for geometric objects called foliations that have a "leaf" structure. Cohomology produces these invariants by considering the global object as patched together from pieces. The successful completion of this project will help complete theclassification problem in geometry. ***