Mathematical Sciences: The Geometry and Topology of         Manifolds
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{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
The problems addressed in this research are in the area of              geometric topology, primarily in low dimensions.  Some of the                   problems concern structures on manifolds, e.g., what sorts of                   triangulations can exist, or what types of metrics, or how can a                manifold be expressed as a quotient of some nice domain?  Other                 questions concern automorphisms of manifolds, e.g., how can they                act, and what is the structure of the full group of                             automorphisms?  This leads to focusing on the groups themselves,                and how they decompose, or how they can act on other simple                     spaces, for example, trees.  Part of the proposal revolves about                an important class of homeomorphisms called quasiconformal                      homeomorphisms, and, in particular, how can certain structure                   changes of manifolds be achieved by quasiconformal deformations,                and what sort of limiting behavior can one find?  There has been                an enormous amount of activity in all of these areas in recent                  years, and there is much opportunity for tying a lot of it                      together.  Opportunities for applications will continue to occur                in theoretical physics and possibly elsewhere.
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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