Mathematical Sciences: Noncommutative Differential Geometry and Topology
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
This project is mathematical research in the theory of                     operator algebras bearing on issues in geometry and topology.                   The operator algebras (or C*-algebras) here are thought of as                   noncommutative analogs of (the algebra of continuous functions                  on) a compact topological space.  Differentiable structure can be               introduced in the form of a C*-dynamical system, with a Lie group               acting on the C*-algebra.                                                            More specifically, one of the goals of the project is to                   establish a Chern-Weil theory for C*-dynamical systems, thereby                 introducing a whole new class of differential and topological                   invariants for noncommutative differentiable manifolds having                   principal fibre structures.  Another problem is to characterize                 the smooth structures of manifolds (commutative or otherwise) in                terms of certain subalgebras and cyclic homology theory.  The                   principal investigator will continue his study of the close                     relationship between dynamical invariants of structurally stable                flows and K-theoretical invariants of flow algebras.
{'FirstName': 'Xiaolu', 'LastName': 'Wang', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Xiaolu Wang', 'EmailAddress': 'xnw@karen.umd.edu', 'NSF_ID': '000326217', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Maryland, College Park', 'CityName': 'COLLEGE PARK', 'ZipCode': '207425100', 'PhoneNumber': '3014056269', 'StreetAddress': '3112 LEE BUILDING', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Maryland', 'StateCode': 'MD', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'MD04', 'ORG_UEI_NUM': 'NPU8ULVAAS23', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF MARYLAND, COLLEGE PARK', 'ORG_PRNT_UEI_NUM': 'NPU8ULVAAS23'}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8805158.xml'}