Mathematical Sciences: Geometric Topology
{'Code': '03040200', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
Birman anticipates the development of an algorithm which                   will begin with two oriented links L and L', represented by                     closed n and r-braids respectively (or alternatively by arbitrary               link diagrams with n and r Seifert circles respectively), and                   which will decide whether these links are isotopic.  For the                    special case where L' is the standard representative of the r-                  component unlink, she expects that the algorithm will be a                      polynomial-time algorithm.                                                           Morgan plans to study compactness questions for families of                hyperbolic n-manifolds, and more generally the problem of                       compactifying such families.  He intends to study the C-infinity                classification of algebraic surfaces using new ideas introduced                 by Donaldson involving gauge theory.                                                 Hodgson's research deals mostly with the investigation of 3-               dimensional manifolds using geometric methods.  His main projects               will involve the study of the hyperbolic Dehn surgery spaces                    introduced by Thurston.  By using techniques including Hodge                    theory and analysis of geometric limits he hopes to obtain new                  results on the local and global structure of these Dehn surgery                 spaces.  This would lead to new methods for constructing                        geometric structures on certain 3-manifolds, for example surface                bundles over the circle.  He also intends to continue his                       investigations into the variation of geometry as hyperbolic                     structures are deformed, especially the kinds of degeneration                   that can occur:  including degeneration to lower dimensional                    limits and splitting along incompressible surfaces.  This will                  include some computational studies involving the construction of                geometric structures on 3-manifolds.  He will also study the new                invariants of 3-manifolds defined recently by Casson and Floer.
[{'FirstName': 'Joan', 'LastName': 'Birman', 'PI_MID_INIT': 'S', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Joan S Birman', 'EmailAddress': 'jb@math.columbia.edu', 'NSF_ID': '000173410', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}, {'FirstName': 'John', 'LastName': 'Morgan', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John W Morgan', 'EmailAddress': 'jmorgan@scgp.stonybrook.edu', 'NSF_ID': '000373980', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}]
{'Name': 'Columbia University', 'CityName': 'NEW YORK', 'ZipCode': '100277922', 'PhoneNumber': '2128546851', 'StreetAddress': '615 W 131ST ST', 'StreetAddress2': 'MC 8741', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '13', 'CONGRESS_DISTRICT_ORG': 'NY13', 'ORG_UEI_NUM': 'F4N1QNPB95M4', 'ORG_LGL_BUS_NAME': 'THE TRUSTEES OF COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1267', 'Text': 'TOPOLOGY'}
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