Mathematical Sciences: Topology
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{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
A computable obstruction theory for existence and uniqueness            of Seifert constructions with general homogeneous spaces as                     typical fiber, has been recently developed by Professors K.B. Lee               and F. Raymond.                                                                         Professor Raymond will refine this theory and develop                   geometric applications.  In particular, the deformation theory of               geometric structures that preserve the fiber structure will be                  studied for various Seifert fiberings and the topology of the                   corresponding moduli spaces will be investigated.                                       Professor Scott will investigate further several problems               centered about three important conjectures that relate the                      topology of 3-manifolds with their fundamental groups.  Consider                closed oriented irreducible 3-manifolds with infinite fundamental               groups.  If M and N are homotopically equivalent, are they                      homeomorphic?  If the fundamental group contains a central                      subgroup isomorphic to the integers, is M a classical Seifert                   3-manifold?  Is the universal covering homeomorphic to Euclidean                space?                                                                                  These topological investigations shed light on the ways in              which geometric objects can be assembled from simpler geometric                 objects.  Solution spaces to algebraic or differential equations                give rise to these same objects, which makes their structural                   properties pervasive and understanding them important.
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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