Mathematical Sciences: Geometric Group Theory and 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}
This program is mainly a study of invariants of not only the            entire class of growth functions of a finitely generated group                  but also particular growth functions within that class.  The                    goals are to extend the class of groups whose growth functions                  are known to be always rational, and to study further the growth                functions that can occur for geometric groups.  The attempt to                  show that rationality of the growth functions is independent of                 the generating set will be in the spirit of Cannon's work.  The                 study of the growth functions that occur will continue the work                 of Floyd and Plotnick on planar groups.  Special attention will                 be paid to reciprocity of the growth functions and to when the                  value at 1 is the reciprocal of the Euler characteristic.  Many                 surprising and easily stated facts about geometric groups have                  been uncovered empirically, and it is time to bring some order                  into the area.
{'FirstName': 'William', 'LastName': 'Floyd', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'William J Floyd', 'EmailAddress': 'floyd@math.vt.edu', 'NSF_ID': '000244963', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Virginia Polytechnic Institute and State University', 'CityName': 'BLACKSBURG', 'ZipCode': '240603359', 'PhoneNumber': '5402315281', 'StreetAddress': '300 TURNER ST NW', 'StreetAddress2': 'STE 4200', 'CountryName': 'United States', 'StateName': 'Virginia', 'StateCode': 'VA', 'CONGRESSDISTRICT': '09', 'CONGRESS_DISTRICT_ORG': 'VA09', 'ORG_UEI_NUM': 'QDE5UHE5XD16', 'ORG_LGL_BUS_NAME': 'VIRGINIA POLYTECHNIC INSTITUTE & STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'M515A1DKXAN8'}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1267', 'Text': 'TOPOLOGY'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701419.xml'}