Mathematical Sciences: Controlled Topology of Manifolds
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Manifolds are the main object of study in topology.  They               are the spaces which are locally homeomorphic to euclidean                      spaces.  Often a manifold E comes equipped with a map p:E--B onto               another manifold which is locally a product projection.  Such a                 map is called a bundle projection.  The controlled topology of E                is the study of certain classical topics in the topology of                     manifolds on which restrictions are placed reflecting the bundle                structure on E. These restrictions usually take the form of                     metric control measured in B.  This project is concerned with the               study of controlled homotopy equivalences, controlled simple                    homotopy theory, and controlled pseudo-isotopies.  These                        technical investigations are important because manifolds are                    ubiquitous in topology, geometry, analysis, even mathematical                   physics.
{'FirstName': 'C. Bruce', 'LastName': 'Hughes', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'C. Bruce Hughes', 'EmailAddress': 'bruce.hughes@vanderbilt.edu', 'NSF_ID': '000249437', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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