Mathematical Sciences: Problems in Low Dimensional Manifolds
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{'SignBlockName': 'Ralph M. Krause', 'PO_EMAI': None, 'PO_PHON': None}
Long plans to examine several interrelated questions in the             theory of low dimensional manifolds and group theory.  The                      specific problems concern general hyperbolic 3-manifolds (whether               their fundamental groups can be subgroup separable), the                        particular case of hyperbolic surface bundles over the circle                   (same question, and other specific questions related to the                     behavior of the entropy and volume functions), and cobordism of                 surface automorphisms (whether there is an algorithm to determine               when a lamination is a limit of discs).  These problems are                     related to Long's established interests in several classical                    problems in the theory of hyperbolic manifolds and knot and                     surface cobordism.                                                                      Geometric topological investigations such as these develop              methods for analysing qualitative properties of geometric                       objects, e.g. knottedness.  In some contexts understanding these                properties is every bit as valuable as understanding rigid metric               properties.
{'FirstName': 'Darren', 'LastName': 'Long', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Darren Long', 'EmailAddress': 'long@math.ucsb.edu', 'NSF_ID': '000469581', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-Santa Barbara', 'CityName': 'SANTA BARBARA', 'ZipCode': '931060001', 'PhoneNumber': '8058934188', 'StreetAddress': '3227 CHEADLE HALL', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '24', 'CONGRESS_DISTRICT_ORG': 'CA24', 'ORG_UEI_NUM': 'G9QBQDH39DF4', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA, SANTA BARBARA', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126700', 'Text': 'TOPOLOGY'}
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